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The phrase "a direct proof" is correct and usable in written English.
It can be used in mathematical or logical contexts to refer to a type of proof that demonstrates the truth of a statement through straightforward reasoning.
Example: "To establish the theorem, we will provide a direct proof that clearly outlines each step of the argument."
Alternatives: "an explicit proof" or "a straightforward proof".
Exact(60)
This is a direct proof of the spherical shape of Earth, a discovery made by the ancient Greeks.
As the scientists themselves carefully noted, "It is important to acknowledge that our research does not provide a direct proof of subjective experience".
She said: "The rape culture of India is a direct proof of complete disregard for women's & girls' rights and bodily integrity".
This result is a direct proof from Theorem 3.1.
We give here a direct proof of the equivalence of statements (h2), (h3) (h5) and (h6).
As a direct proof of Theorem 3.1, we obtain the following results.
A direct proof on the LTS semantics is reported in [19].
Recently, Zhou and his collaborators [7] give a direct proof for McKean's theorem [5].
The present version could also be deduced from the work of Akin [1]; a direct proof is given in [36].
This is a direct proof for less oxygen content for the upper layers of the thicker film.
A direct proof is the contact angle of biodiesel on the surface of G105 steel (Fig. 2).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com