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Theorem e02 38742
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e02.1 𝜑
e02.2 (   𝜓   ,   𝜒   ▶   𝜃   )
e02.3 (𝜑 → (𝜃𝜏))
Assertion
Ref Expression
e02 (   𝜓   ,   𝜒   ▶   𝜏   )

Proof of Theorem e02
StepHypRef Expression
1 e02.1 . . 3 𝜑
21vd02 38643 . 2 (   𝜓   ,   𝜒   ▶   𝜑   )
3 e02.2 . 2 (   𝜓   ,   𝜒   ▶   𝜃   )
4 e02.3 . 2 (𝜑 → (𝜃𝜏))
52, 3, 4e22 38716 1 (   𝜓   ,   𝜒   ▶   𝜏   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 38613
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-an 386  df-vd2 38614
This theorem is referenced by:  e02an  38743  onfrALTlem3VD  38943  vk15.4jVD  38970
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