Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  dfvd3ir Structured version   Visualization version   GIF version

Theorem dfvd3ir 41292
Description: Right-to-left inference form of dfvd3 41290. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
dfvd3ir.1 (𝜑 → (𝜓 → (𝜒𝜃)))
Assertion
Ref Expression
dfvd3ir (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )

Proof of Theorem dfvd3ir
StepHypRef Expression
1 dfvd3ir.1 . 2 (𝜑 → (𝜓 → (𝜒𝜃)))
2 dfvd3 41290 . 2 ((   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   ) ↔ (𝜑 → (𝜓 → (𝜒𝜃))))
31, 2mpbir 234 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd3 41286
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-an 400  df-3an 1086  df-vd3 41289
This theorem is referenced by:  vd03  41298  vd13  41300  vd23  41301  in3an  41310  idn3  41314  gen31  41320  e223  41334  e333  41432  e233  41464  e323  41465
  Copyright terms: Public domain W3C validator