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Theorem e23 41459
Description: A virtual deduction elimination rule (see syl10 79). (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e23.1 (   𝜑   ,   𝜓   ▶   𝜒   )
e23.2 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜏   )
e23.3 (𝜒 → (𝜏𝜂))
Assertion
Ref Expression
e23 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜂   )

Proof of Theorem e23
StepHypRef Expression
1 e23.1 . . 3 (   𝜑   ,   𝜓   ▶   𝜒   )
21vd23 41306 . 2 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜒   )
3 e23.2 . 2 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜏   )
4 e23.3 . 2 (𝜒 → (𝜏𝜂))
52, 3, 4e33 41438 1 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 41281  (   wvd3 41291
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 210  df-an 400  df-3an 1086  df-vd2 41282  df-vd3 41294
This theorem is referenced by:  e23an  41460  suctrALT2VD  41540  rspsbc2VD  41559  tratrbVD  41565  imbi12VD  41577  imbi13VD  41578
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