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Theorem e002 41269
Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e002.1 𝜑
e002.2 𝜓
e002.3 (   𝜒   ,   𝜃   ▶   𝜏   )
e002.4 (𝜑 → (𝜓 → (𝜏𝜂)))
Assertion
Ref Expression
e002 (   𝜒   ,   𝜃   ▶   𝜂   )

Proof of Theorem e002
StepHypRef Expression
1 e002.1 . . 3 𝜑
21vd02 41224 . 2 (   𝜒   ,   𝜃   ▶   𝜑   )
3 e002.2 . . 3 𝜓
43vd02 41224 . 2 (   𝜒   ,   𝜃   ▶   𝜓   )
5 e002.3 . 2 (   𝜒   ,   𝜃   ▶   𝜏   )
6 e002.4 . 2 (𝜑 → (𝜓 → (𝜏𝜂)))
72, 4, 5, 6e222 41262 1 (   𝜒   ,   𝜃   ▶   𝜂   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   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-vd2 41204
This theorem is referenced by: (None)
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