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Theorem e110 39320
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e110.1 (   𝜑   ▶   𝜓   )
e110.2 (   𝜑   ▶   𝜒   )
e110.3 𝜃
e110.4 (𝜓 → (𝜒 → (𝜃𝜏)))
Assertion
Ref Expression
e110 (   𝜑   ▶   𝜏   )

Proof of Theorem e110
StepHypRef Expression
1 e110.1 . 2 (   𝜑   ▶   𝜓   )
2 e110.2 . 2 (   𝜑   ▶   𝜒   )
3 e110.3 . . 3 𝜃
43vd01 39241 . 2 (   𝜑   ▶   𝜃   )
5 e110.4 . 2 (𝜓 → (𝜒 → (𝜃𝜏)))
61, 2, 4, 5e111 39318 1 (   𝜑   ▶   𝜏   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd1 39204
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-vd1 39205
This theorem is referenced by:  2uasbanhVD  39563
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