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Theorem exp516 1135
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 350 . 2 (𝜑 → ((𝜓𝜒𝜃) → (𝜏𝜂)))
323expd 1132 1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by: (None)
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