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Theorem e20 38774
Description: A virtual deduction elimination rule (see syl6mpi 67). (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e20.1 (   𝜑   ,   𝜓   ▶   𝜒   )
e20.2 𝜃
e20.3 (𝜒 → (𝜃𝜏))
Assertion
Ref Expression
e20 (   𝜑   ,   𝜓   ▶   𝜏   )

Proof of Theorem e20
StepHypRef Expression
1 e20.1 . 2 (   𝜑   ,   𝜓   ▶   𝜒   )
2 e20.2 . . 3 𝜃
32vd02 38643 . 2 (   𝜑   ,   𝜓   ▶   𝜃   )
4 e20.3 . 2 (𝜒 → (𝜃𝜏))
51, 3, 4e22 38716 1 (   𝜑   ,   𝜓   ▶   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:  e20an  38775  tratrbVD  38917  onfrALTlem3VD  38943
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