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Theorem e23an 42049
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e23an.1 (   𝜑   ,   𝜓   ▶   𝜒   )
e23an.2 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜏   )
e23an.3 ((𝜒𝜏) → 𝜂)
Assertion
Ref Expression
e23an (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜂   )

Proof of Theorem e23an
StepHypRef Expression
1 e23an.1 . 2 (   𝜑   ,   𝜓   ▶   𝜒   )
2 e23an.2 . 2 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜏   )
3 e23an.3 . . 3 ((𝜒𝜏) → 𝜂)
43ex 416 . 2 (𝜒 → (𝜏𝜂))
51, 2, 4e23 42048 1 (   𝜑   ,   𝜓   ,   𝜃   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  (   wvd2 41870  (   wvd3 41880
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 1091  df-vd2 41871  df-vd3 41883
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator