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Theorem exp44 640
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 630 . 2 (𝜑 → ((𝜓𝜒) → (𝜃𝜏)))
32expd 451 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
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 197  df-an 385
This theorem is referenced by:  wefrc  5137  tz7.7  5787  oalimcl  7685  unbenlem  15659  rnelfm  21804  uspgr2wlkeqi  26600  1pthon2v  27131  spansncvi  28639  atom1d  29340  chirredlem3  29379  conway  32035  finminlem  32437  cvlcvr1  34944  lhpexle2lem  35613  trlord  36174  cdlemkid4  36539  dihord6apre  36862  dihglbcpreN  36906
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