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Theorem e022 42214
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e022.1 𝜑
e022.2 (   𝜓   ,   𝜒   ▶   𝜃   )
e022.3 (   𝜓   ,   𝜒   ▶   𝜏   )
e022.4 (𝜑 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
e022 (   𝜓   ,   𝜒   ▶   𝜂   )

Proof of Theorem e022
StepHypRef Expression
1 e022.1 . . 3 𝜑
21vd02 42171 . 2 (   𝜓   ,   𝜒   ▶   𝜑   )
3 e022.2 . 2 (   𝜓   ,   𝜒   ▶   𝜃   )
4 e022.3 . 2 (   𝜓   ,   𝜒   ▶   𝜏   )
5 e022.4 . 2 (𝜑 → (𝜃 → (𝜏𝜂)))
62, 3, 4, 5e222 42209 1 (   𝜓   ,   𝜒   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd2 42150
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 396  df-vd2 42151
This theorem is referenced by:  onfrALTVD  42464
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