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Theorem e30 39288
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e30.1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
e30.2 𝜏
e30.3 (𝜃 → (𝜏𝜂))
Assertion
Ref Expression
e30 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )

Proof of Theorem e30
StepHypRef Expression
1 e30.1 . 2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜃   )
2 e30.2 . . 3 𝜏
32vd03 39141 . 2 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜏   )
4 e30.3 . 2 (𝜃 → (𝜏𝜂))
51, 3, 4e33 39278 1 (   𝜑   ,   𝜓   ,   𝜒   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd3 39120
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 385  df-3an 1056  df-vd3 39123
This theorem is referenced by:  e30an  39290
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