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Theorem e211 41283
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e211.1 (   𝜑   ,   𝜓   ▶   𝜒   )
e211.2 (   𝜑   ▶   𝜃   )
e211.3 (   𝜑   ▶   𝜏   )
e211.4 (𝜒 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
e211 (   𝜑   ,   𝜓   ▶   𝜂   )

Proof of Theorem e211
StepHypRef Expression
1 e211.1 . 2 (   𝜑   ,   𝜓   ▶   𝜒   )
2 e211.2 . . 3 (   𝜑   ▶   𝜃   )
32vd12 41226 . 2 (   𝜑   ,   𝜓   ▶   𝜃   )
4 e211.3 . . 3 (   𝜑   ▶   𝜏   )
54vd12 41226 . 2 (   𝜑   ,   𝜓   ▶   𝜏   )
6 e211.4 . 2 (𝜒 → (𝜃 → (𝜏𝜂)))
71, 3, 5, 6e222 41262 1 (   𝜑   ,   𝜓   ▶   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:  e210  41285  e201  41287
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