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Theorem e20 41426
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 41297 . 2 (   𝜑   ,   𝜓   ▶   𝜃   )
4 e20.3 . 2 (𝜒 → (𝜃𝜏))
51, 3, 4e22 41370 1 (   𝜑   ,   𝜓   ▶   𝜏   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 41276
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-vd2 41277
This theorem is referenced by:  e20an  41427  tratrbVD  41560  onfrALTlem3VD  41586
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