which establishes that

USAGE SUMMARY

The phrase "which establishes that" is correct and usable in written English.
It can be used to introduce a clause that provides evidence or support for a statement or argument made earlier in the text. Example: "The research findings are significant, which establishes that a correlation exists between the two variables."

✓ Grammatically correct

Science

News & Media

Formal & Business

Human-verified examples from authoritative sources

Exact Expressions

41 human-written examples

So we have that Qd and d≠b, which establishes that Q−bd.

SEP

Recalling from Proposition 2.3 iii) that (Phi^{ prime }) is a homeomorphism, we derive ((u_{n},v_{n})rightarrow (u,v)), which establishes that φ satisfies the Cerami condition.

Boundary Value Problems

Now that Sz and Rz are comparable, hence by (2.1) it is obvious that s^{ varepsilon}d ( fz,gz ) leq M_{s} ( z,z ) =d ( Sz,Rz ) =d ( fz,gz ), which establishes that (fz=gz) (because (s^{ varepsilon}>1)).

Fixed Point Theory and Applications

They also correctly stress the importance of Law 107/2015, now being implemented, which establishes that in-service training is compulsory, structured and continuing for all teachers, including those in VET.

Empirical Research in Vocational Education and Training

The promoted molybdenum sulfided catalysts showed a wide range of activity variation with support composition, which establishes that molybdenum sulfided active phases strongly depend on the nature and composition of the support.

Catalysis Today

SolutionsDuring the last year, in an attempt to put pressure on other European countries to do more, Italian authorities have stopped fingerprinting all the migrants that arrive on their shores — in violation of the Dublin Regulation, which establishes that non-Europeans be registered at their first port of arrival.

Vice

Human-verified similar examples from authoritative sources

Similar Expressions

19 human-written examples

In 2003, she wrote the liberal majority opinion that upheld the University of Michigan Law School's racial-preference programme, which established that diversity in education is a compelling state interest.

The Economist

This began to change with the 1925 enactment of the Federal Arbitration Act, which established that agreements to arbitrate were enforceable like any other contract.

The New York Times

That judgment went further than a High Court ruling of 1992, known as the Mabo case, which established that aborigines had the right to claim native title to traditional lands, something never recognised before.

The Economist

Mora and Philippot provide no scientific evidence of its feasibility, nor it is found in the literature, and it contradicts the instructions found in treatises on fresco, which establish that fresco paintings have to be executed in giornate.

Heritage Science

A handful of discrimination suit victories have gone in favor of transgender workers in the 18 months following the landmark case Macy v. Holder, which established that gender identity is in fact protected under Title VII.

Huffington Post

Expert writing Tips

Best practice

When using "which establishes that", ensure the connection between the clauses is logically sound and evident to the reader. This ensures the strength of your argument and clarity.

Common error

Avoid using "which establishes that" if the connection between the two clauses is merely suggestive or correlational, rather than a direct and definitive proof. Using the phrase when the relationship is weak can weaken your overall argument.

Linguistic Context

The primary grammatical function of "which establishes that" is to introduce a non-restrictive (or non-defining) relative clause. This clause provides additional information that proves or confirms a statement made in the main clause. Ludwig examples highlight the phrase's use in academic and news contexts.

Expression frequency: Very common

Frequent in

Science

75%

News & Media

15%

Formal & Business

5%

Less common in

Wiki

3%

Encyclopedias

1%

Reference

1%

Ludwig's WRAP-UP

The phrase "which establishes that" is a common and grammatically sound way to introduce a clause that provides proof or confirmation for a preceding statement. Ludwig AI confirms its usage across various domains, particularly in science, news media, and formal writing. When using this phrase, it's important to ensure that the connection between the clauses is strong and logically sound, avoiding overstatements. Alternatives like "which demonstrates that" or "which indicates that" can be used depending on the desired level of emphasis. By understanding its function and context, writers can effectively use "which establishes that" to strengthen their arguments and communicate with clarity.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

which demonstrates that

Focuses on showing or proving something through evidence.

which proves that

Emphasizes a conclusive demonstration of truth.

which indicates that

Suggests a sign or signal pointing towards a conclusion.

which confirms that

Highlights the act of verifying or substantiating a claim.

which implies that

Suggests a logical consequence or necessary condition.

which reveals that

Focuses on uncovering something previously unknown.

which validates that

Stresses the act of confirming the accuracy or soundness of something.

which substantiates that

Emphasizes providing evidence to support a claim.

which signifies that

Highlights the meaning or importance of something.

which supports the idea that

Emphasizes contribution to the acceptability of an idea.

FAQs

How can I use "which establishes that" in a sentence?

Use "which establishes that" to connect a clause that provides direct proof or evidence for a preceding statement. For example: "The data shows a clear correlation, which establishes that the hypothesis is supported."

What are some alternatives to "which establishes that"?

You can use alternatives like "which demonstrates that", "which proves that", or "which indicates that depending on the context.

Is it always necessary to use "that" after "which establishes"?

While not always grammatically required, including "that" after "which establishes" often improves clarity and readability, particularly in formal writing.

What's the difference between "which establishes that" and "which suggests that"?

"Which establishes that" indicates a more definitive proof or confirmation, while "which suggests that" implies a weaker, more tentative connection. Use "which establishes that" when the evidence is strong and conclusive.