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Theorem dfvd2ir 33549
Description: Right-to-left inference form of dfvd2 33542. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
dfvd2ir.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
dfvd2ir  |-  (. ph ,. ps  ->.  ch ).

Proof of Theorem dfvd2ir
StepHypRef Expression
1 dfvd2ir.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
2 dfvd2 33542 . 2  |-  ( (.
ph ,. ps  ->.  ch ).  <->  ( ph  ->  ( ps  ->  ch ) ) )
31, 2mpbir 209 1  |-  (. ph ,. ps  ->.  ch ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd2 33540
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 185  df-an 371  df-vd2 33541
This theorem is referenced by:  vd02  33570  vd12  33572  in2an  33580  in3  33581  idn2  33585  gen21  33591  gen21nv  33592  gen22  33594  e2  33603  e222  33608
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