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Theorem in2 36898
Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 2 virtual hypotheses into an antecedent. (Contributed by Alan Sare, 21-Apr-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
in2.1  |-  (. ph ,. ps  ->.  ch ).
Assertion
Ref Expression
in2  |-  (. ph  ->.  ( ps  ->  ch ) ).

Proof of Theorem in2
StepHypRef Expression
1 in2.1 . . 3  |-  (. ph ,. ps  ->.  ch ).
21dfvd2i 36869 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
32dfvd1ir 36857 1  |-  (. ph  ->.  ( ps  ->  ch ) ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd1 36853   (.wvd2 36861
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-vd1 36854  df-vd2 36862
This theorem is referenced by:  e223  36928  trsspwALT  37122  sspwtr  37125  pwtrVD  37136  pwtrrVD  37137  snssiALTVD  37139  sstrALT2VD  37146  suctrALT2VD  37148  elex2VD  37150  elex22VD  37151  eqsbc3rVD  37152  tpid3gVD  37154  en3lplem1VD  37155  en3lplem2VD  37156  3ornot23VD  37159  orbi1rVD  37160  19.21a3con13vVD  37164  exbirVD  37165  exbiriVD  37166  rspsbc2VD  37167  tratrbVD  37174  syl5impVD  37176  ssralv2VD  37179  imbi12VD  37186  imbi13VD  37187  sbcim2gVD  37188  sbcbiVD  37189  truniALTVD  37191  trintALTVD  37193  onfrALTVD  37204  relopabVD  37214  19.41rgVD  37215  hbimpgVD  37217  ax6e2eqVD  37220  ax6e2ndeqVD  37222  con3ALTVD  37229
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