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Theorem exp5o 1158
Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)
Hypothesis
Ref Expression
exp5o.1 ((𝜑𝜓𝜒) → ((𝜃𝜏) → 𝜂))
Assertion
Ref Expression
exp5o (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))

Proof of Theorem exp5o
StepHypRef Expression
1 exp5o.1 . . 3 ((𝜑𝜓𝜒) → ((𝜃𝜏) → 𝜂))
21expd 254 . 2 ((𝜑𝜓𝜒) → (𝜃 → (𝜏𝜂)))
323exp 1138 1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  exp520  1160  bndndx  8354
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