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Theorem imp5p 32430
Description: A triple importation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)
Hypothesis
Ref Expression
3imp5.1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Assertion
Ref Expression
imp5p (𝜑 → (𝜓 → ((𝜒𝜃𝜏) → 𝜂)))

Proof of Theorem imp5p
StepHypRef Expression
1 3imp5.1 . . . 4 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
21com52l 102 . . 3 (𝜒 → (𝜃 → (𝜏 → (𝜑 → (𝜓𝜂)))))
323imp 1275 . 2 ((𝜒𝜃𝜏) → (𝜑 → (𝜓𝜂)))
43com3l 89 1 (𝜑 → (𝜓 → ((𝜒𝜃𝜏) → 𝜂)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1054
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
This theorem is referenced by: (None)
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