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Theorem in2 38650
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 (   𝜑   ,   𝜓   ▶   𝜒   )
Assertion
Ref Expression
in2 (   𝜑   ▶   (𝜓𝜒)   )

Proof of Theorem in2
StepHypRef Expression
1 in2.1 . . 3 (   𝜑   ,   𝜓   ▶   𝜒   )
21dfvd2i 38621 . 2 (𝜑 → (𝜓𝜒))
32dfvd1ir 38609 1 (   𝜑   ▶   (𝜓𝜒)   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 38605  (   wvd2 38613
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 197  df-an 386  df-vd1 38606  df-vd2 38614
This theorem is referenced by:  e223  38680  trsspwALT  38865  sspwtr  38868  pwtrVD  38879  pwtrrVD  38880  snssiALTVD  38882  sstrALT2VD  38889  suctrALT2VD  38891  elex2VD  38893  elex22VD  38894  eqsbc3rVD  38895  tpid3gVD  38897  en3lplem1VD  38898  en3lplem2VD  38899  3ornot23VD  38902  orbi1rVD  38903  19.21a3con13vVD  38907  exbirVD  38908  exbiriVD  38909  rspsbc2VD  38910  tratrbVD  38917  syl5impVD  38919  ssralv2VD  38922  imbi12VD  38929  imbi13VD  38930  sbcim2gVD  38931  sbcbiVD  38932  truniALTVD  38934  trintALTVD  38936  onfrALTVD  38947  relopabVD  38957  19.41rgVD  38958  hbimpgVD  38960  ax6e2eqVD  38963  ax6e2ndeqVD  38965  con3ALTVD  38972
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