ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  exp5c GIF version

Theorem exp5c 362
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
exp5c.1 (𝜑 → ((𝜓𝜒) → ((𝜃𝜏) → 𝜂)))
Assertion
Ref Expression
exp5c (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))

Proof of Theorem exp5c
StepHypRef Expression
1 exp5c.1 . . 3 (𝜑 → ((𝜓𝜒) → ((𝜃𝜏) → 𝜂)))
21exp4a 352 . 2 (𝜑 → ((𝜓𝜒) → (𝜃 → (𝜏𝜂))))
32expd 249 1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
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
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator