ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  exp53 GIF version

Theorem exp53 375
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 114 . 2 (((𝜑𝜓) ∧ (𝜒𝜃)) → (𝜏𝜂))
32exp43 370 1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  xpdom2  6776  elfzodifsumelfzo  10100
  Copyright terms: Public domain W3C validator