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Theorem e112 41280
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e112.1 (   𝜑   ▶   𝜓   )
e112.2 (   𝜑   ▶   𝜒   )
e112.3 (   𝜑   ,   𝜃   ▶   𝜏   )
e112.4 (𝜓 → (𝜒 → (𝜏𝜂)))
Assertion
Ref Expression
e112 (   𝜑   ,   𝜃   ▶   𝜂   )

Proof of Theorem e112
StepHypRef Expression
1 e112.1 . . 3 (   𝜑   ▶   𝜓   )
21vd12 41226 . 2 (   𝜑   ,   𝜃   ▶   𝜓   )
3 e112.2 . . 3 (   𝜑   ▶   𝜒   )
43vd12 41226 . 2 (   𝜑   ,   𝜃   ▶   𝜒   )
5 e112.3 . 2 (   𝜑   ,   𝜃   ▶   𝜏   )
6 e112.4 . 2 (𝜓 → (𝜒 → (𝜏𝜂)))
72, 4, 5, 6e222 41262 1 (   𝜑   ,   𝜃   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 41195  (   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-vd1 41196  df-vd2 41204
This theorem is referenced by:  e012  41293  e102  41295
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