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Theorem exp520 1279
Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)
Hypothesis
Ref Expression
exp520.1 (((𝜑𝜓𝜒) ∧ (𝜃𝜏)) → 𝜂)
Assertion
Ref Expression
exp520 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))

Proof of Theorem exp520
StepHypRef Expression
1 exp520.1 . . 3 (((𝜑𝜓𝜒) ∧ (𝜃𝜏)) → 𝜂)
21ex 448 . 2 ((𝜑𝜓𝜒) → ((𝜃𝜏) → 𝜂))
32exp5o 1277 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:  omwordri  7516  oewordri  7536  lcmfunsnlem2  15137  pclfinclN  34057
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