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Theorem exp53 646
Description: An exportation inference. (Contributed by Jeff Hankins, 30-Aug-2009.)
Hypothesis
Ref Expression
exp53.1 ((((𝜑𝜓) ∧ (𝜒𝜃)) ∧ 𝜏) → 𝜂)
Assertion
Ref Expression
exp53 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))

Proof of Theorem exp53
StepHypRef Expression
1 exp53.1 . . 3 ((((𝜑𝜓) ∧ (𝜒𝜃)) ∧ 𝜏) → 𝜂)
21ex 450 . 2 (((𝜑𝜓) ∧ (𝜒𝜃)) → (𝜏𝜂))
32exp43 639 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:  omordi  7591  xpdom2  7999  elfzodifsumelfzo  12474  grplcan  17398  grpolcan  27230
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