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Theorem expt 593
Description: Exportation theorem expressed with primitive connectives. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
expt ((¬ (𝜑 → ¬ 𝜓) → 𝜒) → (𝜑 → (𝜓𝜒)))

Proof of Theorem expt
StepHypRef Expression
1 pm3.2im 576 . . 3 (𝜑 → (𝜓 → ¬ (𝜑 → ¬ 𝜓)))
21imim1d 73 . 2 (𝜑 → ((¬ (𝜑 → ¬ 𝜓) → 𝜒) → (𝜓𝜒)))
32com12 30 1 ((¬ (𝜑 → ¬ 𝜓) → 𝜒) → (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 554  ax-in2 555
This theorem is referenced by: (None)
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