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Theorem exp5d 31965
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
exp5d.1 (((𝜑𝜓) ∧ 𝜒) → ((𝜃𝜏) → 𝜂))
Assertion
Ref Expression
exp5d (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))

Proof of Theorem exp5d
StepHypRef Expression
1 exp5d.1 . . 3 (((𝜑𝜓) ∧ 𝜒) → ((𝜃𝜏) → 𝜂))
21expd 452 . 2 (((𝜑𝜓) ∧ 𝜒) → (𝜃 → (𝜏𝜂)))
32exp31 629 1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
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 197  df-an 386
This theorem is referenced by:  exp56  31968
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