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Theorem e12 38771
Description: A virtual deduction elimination rule (see sylsyld 61). (Contributed by Alan Sare, 21-Apr-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e12.1 (   𝜑   ▶   𝜓   )
e12.2 (   𝜑   ,   𝜒   ▶   𝜃   )
e12.3 (𝜓 → (𝜃𝜏))
Assertion
Ref Expression
e12 (   𝜑   ,   𝜒   ▶   𝜏   )

Proof of Theorem e12
StepHypRef Expression
1 e12.1 . . 3 (   𝜑   ▶   𝜓   )
21vd12 38645 . 2 (   𝜑   ,   𝜒   ▶   𝜓   )
3 e12.2 . 2 (   𝜑   ,   𝜒   ▶   𝜃   )
4 e12.3 . 2 (𝜓 → (𝜃𝜏))
52, 3, 4e22 38716 1 (   𝜑   ,   𝜒   ▶   𝜏   )
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:  e12an  38772  trsspwALT  38865  sspwtr  38868  pwtrVD  38879  snssiALTVD  38882  elex2VD  38893  elex22VD  38894  eqsbc3rVD  38895  en3lplem1VD  38898  3ornot23VD  38902  orbi1rVD  38903  19.21a3con13vVD  38907  exbirVD  38908  tratrbVD  38917  ssralv2VD  38922  sbcim2gVD  38931  sbcbiVD  38932  relopabVD  38957  19.41rgVD  38958  ax6e2eqVD  38963  ax6e2ndeqVD  38965  vk15.4jVD  38970  con3ALTVD  38972
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