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Theorem e21 44755
Description: A virtual deduction elimination rule (see syl6ci 71). (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e21.1 (   𝜑   ,   𝜓   ▶   𝜒   )
e21.2 (   𝜑   ▶   𝜃   )
e21.3 (𝜒 → (𝜃𝜏))
Assertion
Ref Expression
e21 (   𝜑   ,   𝜓   ▶   𝜏   )

Proof of Theorem e21
StepHypRef Expression
1 e21.1 . 2 (   𝜑   ,   𝜓   ▶   𝜒   )
2 e21.2 . . 3 (   𝜑   ▶   𝜃   )
32vd12 44625 . 2 (   𝜑   ,   𝜓   ▶   𝜃   )
4 e21.3 . 2 (𝜒 → (𝜃𝜏))
51, 3, 4e22 44696 1 (   𝜑   ,   𝜓   ▶   𝜏   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 44594  (   wvd2 44602
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 207  df-an 396  df-vd1 44595  df-vd2 44603
This theorem is referenced by:  e21an  44756  en3lplem1VD  44868  exbiriVD  44879  syl5impVD  44888  sbcim2gVD  44900  onfrALTlem3VD  44912  onfrALTlem2VD  44914  hbimpgVD  44929  ax6e2eqVD  44932  vk15.4jVD  44939
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