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Theorem exp516 1278
Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)
Hypothesis
Ref Expression
exp516.1 (((𝜑 ∧ (𝜓𝜒𝜃)) ∧ 𝜏) → 𝜂)
Assertion
Ref Expression
exp516 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))

Proof of Theorem exp516
StepHypRef Expression
1 exp516.1 . . 3 (((𝜑 ∧ (𝜓𝜒𝜃)) ∧ 𝜏) → 𝜂)
21exp31 627 . 2 (𝜑 → ((𝜓𝜒𝜃) → (𝜏𝜂)))
323expd 1275 1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  w3a 1030
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 195  df-an 384  df-3an 1032
This theorem is referenced by: (None)
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