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Theorem e31 38798
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e31.1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
e31.2 (   𝜑   ▶   𝜏   )
e31.3 (𝜃 → (𝜏𝜂))
Assertion
Ref Expression
e31 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )

Proof of Theorem e31
StepHypRef Expression
1 e31.1 . 2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
2 e31.2 . . 3 (   𝜑   ▶   𝜏   )
32vd13 38646 . 2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )
4 e31.3 . 2 (𝜃 → (𝜏𝜂))
51, 3, 4e33 38781 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 38605  (   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-vd1 38606  df-vd3 38626
This theorem is referenced by:  e31an  38800  trintALTVD  38936
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