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Theorem e22 38722
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 2-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e22.1 (   𝜑   ,   𝜓   ▶   𝜒   )
e22.2 (   𝜑   ,   𝜓   ▶   𝜃   )
e22.3 (𝜒 → (𝜃𝜏))
Assertion
Ref Expression
e22 (   𝜑   ,   𝜓   ▶   𝜏   )

Proof of Theorem e22
StepHypRef Expression
1 e22.1 . 2 (   𝜑   ,   𝜓   ▶   𝜒   )
2 e22.2 . 2 (   𝜑   ,   𝜓   ▶   𝜃   )
3 e22.3 . . 3 (𝜒 → (𝜃𝜏))
43a1i 11 . 2 (𝜒 → (𝜒 → (𝜃𝜏)))
51, 1, 2, 4e222 38687 1 (   𝜑   ,   𝜓   ▶   𝜏   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 38619
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-vd2 38620
This theorem is referenced by:  e22an  38723  e02  38748  e12  38777  e20  38780  e21  38783  sspwtr  38874  pwtrVD  38885  pwtrrVD  38886  elex22VD  38900  tpid3gVD  38903  en3lplem2VD  38905  imbi12VD  38935  truniALTVD  38940  trintALTVD  38942  onfrALTlem3VD  38949  onfrALTlem2VD  38951  ax6e2eqVD  38969  ax6e2ndeqVD  38971  sb5ALTVD  38975
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