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Theorem imp5a 581
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 → ((θ τ) → η))))

Proof of Theorem imp5a
StepHypRef Expression
1 imp5.1 . 2 (φ → (ψ → (χ → (θ → (τη)))))
2 pm3.31 432 . 2 ((θ → (τη)) → ((θ τ) → η))
31, 2syl8 65 1 (φ → (ψ → (χ → ((θ τ) → η))))
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358
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 177  df-an 360
This theorem is referenced by: (None)
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