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Theorem expi 567
Description: An exportation inference. (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 28-Nov-2008.)
Hypothesis
Ref Expression
expi.1 (¬ (𝜑 → ¬ 𝜓) → 𝜒)
Assertion
Ref Expression
expi (𝜑 → (𝜓𝜒))

Proof of Theorem expi
StepHypRef Expression
1 pm3.2im 566 . 2 (𝜑 → (𝜓 → ¬ (𝜑 → ¬ 𝜓)))
2 expi.1 . 2 (¬ (𝜑 → ¬ 𝜓) → 𝜒)
31, 2syl6 29 1 (𝜑 → (𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 544  ax-in2 545
This theorem is referenced by:  bj-nn0suc0  9948
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