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Theorem exp512 32809
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
exp512.1 ((𝜑 ∧ ((𝜓𝜒) ∧ (𝜃𝜏))) → 𝜂)
Assertion
Ref Expression
exp512 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))

Proof of Theorem exp512
StepHypRef Expression
1 exp512.1 . . 3 ((𝜑 ∧ ((𝜓𝜒) ∧ (𝜃𝜏))) → 𝜂)
21ex 402 . 2 (𝜑 → (((𝜓𝜒) ∧ (𝜃𝜏)) → 𝜂))
32exp5l 438 1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 385
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 199  df-an 386
This theorem is referenced by: (None)
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