P is a one-place predicate,(adsbygoogle = window.adsbygoogle || []).push({}); tis a constant,vis a variable of P. P(t/v) denotes replacingvbytin P.

In the proof of a theorem, it is given that

Δ[itex]\vdash[/itex][itex]\forall[/itex]vP.

(meaning [itex]\forall[/itex]vP is deduced from the set of statements Δ.)

There exists an axiom scheme

[itex]\vdash[/itex]\forall[/itex]vP[itex]\rightarrow[/itex](P(t/v).

Then modus ponens is applied to these two to prove that

Δ[itex]\vdash[/itex]P(t/v).

I've never seen modus ponens applied to a deduction and it is used with so I scarcely know what to ask...how is this permissible? How does it work...same as regular modus ponens? Is there a proof that this is shows this is the same as modus ponens, or a definition that describes it?

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# Modus Ponens on A Deduction?

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