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Theorem e210 41289
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e210.1 (   𝜑   ,   𝜓   ▶   𝜒   )
e210.2 (   𝜑   ▶   𝜃   )
e210.3 𝜏
e210.4 (𝜒 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
e210 (   𝜑   ,   𝜓   ▶   𝜂   )

Proof of Theorem e210
StepHypRef Expression
1 e210.1 . 2 (   𝜑   ,   𝜓   ▶   𝜒   )
2 e210.2 . 2 (   𝜑   ▶   𝜃   )
3 e210.3 . . 3 𝜏
43vd01 41227 . 2 (   𝜑   ▶   𝜏   )
5 e210.4 . 2 (𝜒 → (𝜃 → (𝜏𝜂)))
61, 2, 4, 5e211 41287 1 (   𝜑   ,   𝜓   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 41199  (   wvd2 41207
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 41200  df-vd2 41208
This theorem is referenced by: (None)
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