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Theorem exp45 438
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
exp45.1 ((𝜑 ∧ (𝜓 ∧ (𝜒𝜃))) → 𝜏)
Assertion
Ref Expression
exp45 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))

Proof of Theorem exp45
StepHypRef Expression
1 exp45.1 . . 3 ((𝜑 ∧ (𝜓 ∧ (𝜒𝜃))) → 𝜏)
21exp32 420 . 2 (𝜑 → (𝜓 → ((𝜒𝜃) → 𝜏)))
32exp4a 431 1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395
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 207  df-an 396
This theorem is referenced by:  oaass  8600  zorn2lem4  10540  zorn2lem7  10543  iscatd2  17725  fgss2  23883  alexsubALTlem4  24059  grporcan  30538  spansncvi  31672  mdsymlem5  32427  riotasv3d  38962  cvratlem  39424  hbtlem2  43141
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