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Theorem exp5c 373
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
exp5c.1 (𝜑 → ((𝜓𝜒) → ((𝜃𝜏) → 𝜂)))
Assertion
Ref Expression
exp5c (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))

Proof of Theorem exp5c
StepHypRef Expression
1 exp5c.1 . . 3 (𝜑 → ((𝜓𝜒) → ((𝜃𝜏) → 𝜂)))
21exp4a 363 . 2 (𝜑 → ((𝜓𝜒) → (𝜃 → (𝜏𝜂))))
32expd 256 1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  fiintim  6785
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