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Theorem e020 41271
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e020.1 𝜑
e020.2 (   𝜓   ,   𝜒   ▶   𝜃   )
e020.3 𝜏
e020.4 (𝜑 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
e020 (   𝜓   ,   𝜒   ▶   𝜂   )

Proof of Theorem e020
StepHypRef Expression
1 e020.1 . . 3 𝜑
21vd02 41224 . 2 (   𝜓   ,   𝜒   ▶   𝜑   )
3 e020.2 . 2 (   𝜓   ,   𝜒   ▶   𝜃   )
4 e020.3 . . 3 𝜏
54vd02 41224 . 2 (   𝜓   ,   𝜒   ▶   𝜏   )
6 e020.4 . 2 (𝜑 → (𝜃 → (𝜏𝜂)))
72, 3, 5, 6e222 41262 1 (   𝜓   ,   𝜒   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 41203
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 41204
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator