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Theorem in3 31628
Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 3 virtual hypotheses into an antecedent. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
in3.1  |-  (. ph ,. ps ,. ch  ->.  th ).
Assertion
Ref Expression
in3  |-  (. ph ,. ps  ->.  ( ch  ->  th ) ).

Proof of Theorem in3
StepHypRef Expression
1 in3.1 . . 3  |-  (. ph ,. ps ,. ch  ->.  th ).
21dfvd3i 31602 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32dfvd2ir 31596 1  |-  (. ph ,. ps  ->.  ( ch  ->  th ) ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd2 31587   (.wvd3 31597
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-3an 967  df-vd2 31588  df-vd3 31600
This theorem is referenced by:  e223  31654  suctrALT2VD  31869  en3lplem2VD  31877  exbirVD  31886  exbiriVD  31887  rspsbc2VD  31888  tratrbVD  31894  ssralv2VD  31899  imbi12VD  31906  imbi13VD  31907  truniALTVD  31911  trintALTVD  31913  onfrALTlem2VD  31922
  Copyright terms: Public domain W3C validator