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Theorem e03 38787
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e03.1 𝜑
e03.2 (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜏   )
e03.3 (𝜑 → (𝜏𝜂))
Assertion
Ref Expression
e03 (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜂   )

Proof of Theorem e03
StepHypRef Expression
1 e03.1 . . 3 𝜑
21vd03 38644 . 2 (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜑   )
3 e03.2 . 2 (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜏   )
4 e03.3 . 2 (𝜑 → (𝜏𝜂))
52, 3, 4e33 38781 1 (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd3 38623
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-3an 1038  df-vd3 38626
This theorem is referenced by:  e03an  38789  suctrALT2VD  38891
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