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Theorem e32 38811
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e32.1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
e32.2 (   𝜑   ,   𝜓   ▶   𝜏   )
e32.3 (𝜃 → (𝜏𝜂))
Assertion
Ref Expression
e32 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )

Proof of Theorem e32
StepHypRef Expression
1 e32.1 . 2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
2 e32.2 . . 3 (   𝜑   ,   𝜓   ▶   𝜏   )
32vd23 38653 . 2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )
4 e32.3 . 2 (𝜃 → (𝜏𝜂))
51, 3, 4e33 38787 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 38619  (   wvd3 38629
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 1039  df-vd2 38620  df-vd3 38632
This theorem is referenced by:  e32an  38813  exbirVD  38914  exbiriVD  38915  ssralv2VD  38928  trintALTVD  38942
  Copyright terms: Public domain W3C validator