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Theorem dfvd2anir 39325
Description: Right-to-left inference form of dfvd2an 39323. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
dfvd2anir.1 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
dfvd2anir (   (   𝜑   ,   𝜓   )   ▶   𝜒   )

Proof of Theorem dfvd2anir
StepHypRef Expression
1 dfvd2anir.1 . 2 ((𝜑𝜓) → 𝜒)
2 dfvd2an 39323 . 2 ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((𝜑𝜓) → 𝜒))
31, 2mpbir 221 1 (   (   𝜑   ,   𝜓   )   ▶   𝜒   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  (   wvd1 39310  (   wvhc2 39321
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-vd1 39311  df-vhc2 39322
This theorem is referenced by:  int3  39362  el021old  39451  el2122old  39469  el12  39478
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