Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  dfvd2anir Structured version   Visualization version   GIF version

Theorem dfvd2anir 41726
Description: Right-to-left inference form of dfvd2an 41724. (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 41724 . 2 ((   (   𝜑   ,   𝜓   )   ▶   𝜒   ) ↔ ((𝜑𝜓) → 𝜒))
31, 2mpbir 234 1 (   (   𝜑   ,   𝜓   )   ▶   𝜒   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  (   wvd1 41711  (   wvhc2 41722
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 210  df-vd1 41712  df-vhc2 41723
This theorem is referenced by:  int3  41754  el021old  41843  el2122old  41861  el12  41868
  Copyright terms: Public domain W3C validator