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Theorem dfvd2ir 40804
Description: Right-to-left inference form of dfvd2 40797. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
dfvd2ir.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
dfvd2ir (   𝜑   ,   𝜓   ▶   𝜒   )

Proof of Theorem dfvd2ir
StepHypRef Expression
1 dfvd2ir.1 . 2 (𝜑 → (𝜓𝜒))
2 dfvd2 40797 . 2 ((   𝜑   ,   𝜓   ▶   𝜒   ) ↔ (𝜑 → (𝜓𝜒)))
31, 2mpbir 232 1 (   𝜑   ,   𝜓   ▶   𝜒   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 40795
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 208  df-an 397  df-vd2 40796
This theorem is referenced by:  vd02  40816  vd12  40818  in2an  40826  in3  40827  idn2  40831  gen21  40837  gen21nv  40838  gen22  40840  e2  40849  e222  40854
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