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Theorem e010 39328
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e010.1 𝜑
e010.2 (   𝜓   ▶   𝜒   )
e010.3 𝜃
e010.4 (𝜑 → (𝜒 → (𝜃𝜏)))
Assertion
Ref Expression
e010 (   𝜓   ▶   𝜏   )

Proof of Theorem e010
StepHypRef Expression
1 e010.1 . . 3 𝜑
21vd01 39241 . 2 (   𝜓   ▶   𝜑   )
3 e010.2 . 2 (   𝜓   ▶   𝜒   )
4 e010.3 . . 3 𝜃
54vd01 39241 . 2 (   𝜓   ▶   𝜃   )
6 e010.4 . 2 (𝜑 → (𝜒 → (𝜃𝜏)))
72, 3, 5, 6e111 39318 1 (   𝜓   ▶   𝜏   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 39204
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-vd1 39205
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator