MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  exp44 Structured version   Visualization version   GIF version

Theorem exp44 438
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
exp44.1 ((𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)) → 𝜏)
Assertion
Ref Expression
exp44 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))

Proof of Theorem exp44
StepHypRef Expression
1 exp44.1 . . 3 ((𝜑 ∧ ((𝜓𝜒) ∧ 𝜃)) → 𝜏)
21exp32 421 . 2 (𝜑 → ((𝜓𝜒) → (𝜃𝜏)))
32expd 416 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396
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 208  df-an 397
This theorem is referenced by:  wefrc  5444  tz7.7  6099  oalimcl  8043  unbenlem  16077  rnelfm  22249  uspgr2wlkeqi  27116  1pthon2v  27618  spansncvi  29116  atom1d  29817  chirredlem3  29856  conway  32875  finminlem  33277  cvlcvr1  36027  lhpexle2lem  36697  trlord  37257  cdlemkid4  37622  dihord6apre  37944  dihglbcpreN  37988
  Copyright terms: Public domain W3C validator