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Theorem vd03 39141
Description: A theorem is virtually inferred by the 3 virtual hypotheses. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
vd03.1 𝜑
Assertion
Ref Expression
vd03 (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜑   )

Proof of Theorem vd03
StepHypRef Expression
1 vd03.1 . . . . 5 𝜑
21a1i 11 . . . 4 (𝜃𝜑)
32a1i 11 . . 3 (𝜒 → (𝜃𝜑))
43a1i 11 . 2 (𝜓 → (𝜒 → (𝜃𝜑)))
54dfvd3ir 39126 1 (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜑   )
Colors of variables: wff setvar class
Syntax hints:  wi 4  (   wvd3 39120
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-an 385  df-3an 1056  df-vd3 39123
This theorem is referenced by:  e03  39284  e30  39288
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