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Theorem e121 39198
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e121.1 (   𝜑   ▶   𝜓   )
e121.2 (   𝜑   ,   𝜒   ▶   𝜃   )
e121.3 (   𝜑   ▶   𝜏   )
e121.4 (𝜓 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
e121 (   𝜑   ,   𝜒   ▶   𝜂   )

Proof of Theorem e121
StepHypRef Expression
1 e121.1 . . 3 (   𝜑   ▶   𝜓   )
21vd12 39142 . 2 (   𝜑   ,   𝜒   ▶   𝜓   )
3 e121.2 . 2 (   𝜑   ,   𝜒   ▶   𝜃   )
4 e121.3 . . 3 (   𝜑   ▶   𝜏   )
54vd12 39142 . 2 (   𝜑   ,   𝜒   ▶   𝜏   )
6 e121.4 . 2 (𝜓 → (𝜃 → (𝜏𝜂)))
72, 3, 5, 6e222 39178 1 (   𝜑   ,   𝜒   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 39102  (   wvd2 39110
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 39103  df-vd2 39111
This theorem is referenced by:  e021  39207  tratrbVD  39411
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