Sentence examples for yields the proposition from inspiring English sources

For example, in ϕx, in which both variables are free, each variable must be replaced appropriately if a proposition of the form in question (such as "Socrates is wise") is to be obtained; but in (∃x)ϕx, in which x is bound, it is necessary only to replace ϕ by a predicate in order to obtain a complete proposition (e.g., replacing ϕ by "is wise" yields the proposition "Something is wise").

This yields the proposition.

The above immediately yields the following proposition.

Then summarizing the above analysis yields the following proposition.

end{aligned}The same proof as that of Theorem 4 yields the following proposition.

Now, explicit computations, using Remark 2, yield the following propositions.

B is a function that, when applied to the semantic value of an appropriate term answer to the question, yields a proposition.

This together with (73), the estimate of K 3 4 − ε 4 ( t ) in Proposition 3.5 in the next subsection, it yields the L ∞ -estimate in Proposition 3.4.

Reversing the order of the terms yields the simple converse of a proposition, but when in addition an A proposition is changed to an I, or an E to an O, the result is called the limited converse of the original.

For unmatched subchannels, the description in Proposition 1 yields the six inequalities in [17, Theorem  2].

end{aligned} (6)In this case, Proposition 1.1 yields the following.