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Theorem imp5a 623
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 pm3.31 461 . 2 ((𝜃 → (𝜏𝜂)) → ((𝜃𝜏) → 𝜂))
31, 2syl8 76 1 (𝜑 → (𝜓 → (𝜒 → ((𝜃𝜏) → 𝜂))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
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 386
This theorem is referenced by:  prtlem17  33680  tendospcanN  35831
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