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Theorem e13 43441
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e13.1 (   𝜑   ▶   𝜓   )
e13.2 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜏   )
e13.3 (𝜓 → (𝜏𝜂))
Assertion
Ref Expression
e13 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜂   )

Proof of Theorem e13
StepHypRef Expression
1 e13.1 . . 3 (   𝜑   ▶   𝜓   )
21vd13 43294 . 2 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜓   )
3 e13.2 . 2 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜏   )
4 e13.3 . 2 (𝜓 → (𝜏𝜂))
52, 3, 4e33 43427 1 (   𝜑   ,   𝜒   ,   𝜃   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 43262  (   wvd3 43280
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 206  df-an 398  df-3an 1090  df-vd1 43263  df-vd3 43283
This theorem is referenced by:  e13an  43442  en3lplem2VD  43537  rspsbc2VD  43548  ssralv2VD  43559  imbi12VD  43566  imbi13VD  43567  truniALTVD  43571
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