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Theorem e220 42219
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e220.1 (   𝜑   ,   𝜓   ▶   𝜒   )
e220.2 (   𝜑   ,   𝜓   ▶   𝜃   )
e220.3 𝜏
e220.4 (𝜒 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
e220 (   𝜑   ,   𝜓   ▶   𝜂   )

Proof of Theorem e220
StepHypRef Expression
1 e220.1 . 2 (   𝜑   ,   𝜓   ▶   𝜒   )
2 e220.2 . 2 (   𝜑   ,   𝜓   ▶   𝜃   )
3 e220.3 . . 3 𝜏
43vd02 42180 . 2 (   𝜑   ,   𝜓   ▶   𝜏   )
5 e220.4 . 2 (𝜒 → (𝜃 → (𝜏𝜂)))
61, 2, 4, 5e222 42218 1 (   𝜑   ,   𝜓   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 42159
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 206  df-an 397  df-vd2 42160
This theorem is referenced by:  e120  42245
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