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Theorem exp45 439
 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 421 . 2 (𝜑 → (𝜓 → ((𝜒𝜃) → 𝜏)))
32exp4a 432 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:  oaass  8044  zorn2lem4  9774  zorn2lem7  9777  iscatd2  16785  fgss2  22170  alexsubALTlem4  22346  grporcan  27982  spansncvi  29116  mdsymlem5  29871  riotasv3d  35648  cvratlem  36109  hbtlem2  39230
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