Users' Mathboxes Mathbox for Jeff Hankins < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  exp5g Structured version   Visualization version   GIF version

Theorem exp5g 31467
Description: An exportation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
exp5g.1 ((𝜑𝜓) → (((𝜒𝜃) ∧ 𝜏) → 𝜂))
Assertion
Ref Expression
exp5g (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))

Proof of Theorem exp5g
StepHypRef Expression
1 exp5g.1 . . 3 ((𝜑𝜓) → (((𝜒𝜃) ∧ 𝜏) → 𝜂))
21exp4c 634 . 2 ((𝜑𝜓) → (𝜒 → (𝜃 → (𝜏𝜂))))
32ex 449 1 (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂)))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383
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 196  df-an 385
This theorem is referenced by:  exp58  31470
  Copyright terms: Public domain W3C validator