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Theorem in3 36626
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 36600 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32dfvd2ir 36594 1  |-  (. ph ,. ps  ->.  ( ch  ->  th ) ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd2 36585   (.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-vd2 36586  df-vd3 36598
This theorem is referenced by:  e223  36652  suctrALT2VD  36872  en3lplem2VD  36880  exbirVD  36889  exbiriVD  36890  rspsbc2VD  36891  tratrbVD  36898  ssralv2VD  36903  imbi12VD  36910  imbi13VD  36911  truniALTVD  36915  trintALTVD  36917  onfrALTlem2VD  36926
  Copyright terms: Public domain W3C validator