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Theorem in3 33808
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 33782 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32dfvd2ir 33776 1  |-  (. ph ,. ps  ->.  ( ch  ->  th ) ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd2 33767   (.wvd3 33777
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 369  df-3an 973  df-vd2 33768  df-vd3 33780
This theorem is referenced by:  e223  33834  suctrALT2VD  34055  en3lplem2VD  34063  exbirVD  34072  exbiriVD  34073  rspsbc2VD  34074  tratrbVD  34081  ssralv2VD  34086  imbi12VD  34093  imbi13VD  34094  truniALTVD  34098  trintALTVD  34100  onfrALTlem2VD  34109
  Copyright terms: Public domain W3C validator