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

Theorem dfvd3ir 36601
Description: Right-to-left inference form of dfvd3 36599. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
dfvd3ir.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
Assertion
Ref Expression
dfvd3ir  |-  (. ph ,. ps ,. ch  ->.  th ).

Proof of Theorem dfvd3ir
StepHypRef Expression
1 dfvd3ir.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
2 dfvd3 36599 . 2  |-  ( (.
ph ,. ps ,. ch  ->.  th ).  <->  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) ) )
31, 2mpbir 212 1  |-  (. ph ,. ps ,. ch  ->.  th ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd3 36595
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 188  df-an 372  df-3an 984  df-vd3 36598
This theorem is referenced by:  vd03  36616  vd13  36618  vd23  36619  in3an  36628  idn3  36632  gen31  36638  e223  36652  e333  36760  e233  36792  e323  36793
  Copyright terms: Public domain W3C validator