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Theorem e120 39390
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 10-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e120.1 (   𝜑   ▶   𝜓   )
e120.2 (   𝜑   ,   𝜒   ▶   𝜃   )
e120.3 𝜏
e120.4 (𝜓 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
e120 (   𝜑   ,   𝜒   ▶   𝜂   )

Proof of Theorem e120
StepHypRef Expression
1 e120.1 . . 3 (   𝜑   ▶   𝜓   )
21vd12 39327 . 2 (   𝜑   ,   𝜒   ▶   𝜓   )
3 e120.2 . 2 (   𝜑   ,   𝜒   ▶   𝜃   )
4 e120.3 . 2 𝜏
5 e120.4 . 2 (𝜓 → (𝜃 → (𝜏𝜂)))
62, 3, 4, 5e220 39364 1 (   𝜑   ,   𝜒   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 39287  (   wvd2 39295
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-vd1 39288  df-vd2 39296
This theorem is referenced by:  pwtrrVD  39559
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