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Theorem exp5l 647
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
exp5l.1 (𝜑 → (((𝜓𝜒) ∧ (𝜃𝜏)) → 𝜂))
Assertion
Ref Expression
exp5l (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))

Proof of Theorem exp5l
StepHypRef Expression
1 exp5l.1 . . 3 (𝜑 → (((𝜓𝜒) ∧ (𝜃𝜏)) → 𝜂))
21expd 451 . 2 (𝜑 → ((𝜓𝜒) → ((𝜃𝜏) → 𝜂)))
32exp5c 645 1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383
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
This theorem is referenced by:  erclwwlktr  27066  erclwwlkntr  27123  exp512  32530
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