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Theorem imp5a 344
Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
imp5.1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Assertion
Ref Expression
imp5a (𝜑 → (𝜓 → (𝜒 → ((𝜃𝜏) → 𝜂))))

Proof of Theorem imp5a
StepHypRef Expression
1 imp5.1 . 2 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
2 pm3.31 253 . 2 ((𝜃 → (𝜏𝜂)) → ((𝜃𝜏) → 𝜂))
31, 2syl8 69 1 (𝜑 → (𝜓 → (𝜒 → ((𝜃𝜏) → 𝜂))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104
This theorem is referenced by: (None)
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