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Theorem exp4d 636
 Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
exp4d.1 (𝜑 → ((𝜓 ∧ (𝜒𝜃)) → 𝜏))
Assertion
Ref Expression
exp4d (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))

Proof of Theorem exp4d
StepHypRef Expression
1 exp4d.1 . . 3 (𝜑 → ((𝜓 ∧ (𝜒𝜃)) → 𝜏))
21expd 451 . 2 (𝜑 → (𝜓 → ((𝜒𝜃) → 𝜏)))
32exp4a 632 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:  tfrlem9  7526  omass  7705  pssnn  8219  cardinfima  8958  ltexprlem7  9902  facdiv  13114  infpnlem1  15661  atcvatlem  29372  mdsymlem5  29394  mdsymlem7  29396  btwnconn1lem11  32329  exp5k  32423
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