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Theorem exp510 32676
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
exp510.1 ((𝜑 ∧ (((𝜓𝜒) ∧ 𝜃) ∧ 𝜏)) → 𝜂)
Assertion
Ref Expression
exp510 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))

Proof of Theorem exp510
StepHypRef Expression
1 exp510.1 . . 3 ((𝜑 ∧ (((𝜓𝜒) ∧ 𝜃) ∧ 𝜏)) → 𝜂)
21ex 401 . 2 (𝜑 → ((((𝜓𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜂))
32exp5j 436 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 198  df-an 385
This theorem is referenced by: (None)
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