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Theorem expt 168
Description: Exportation theorem ex 449 expressed with primitive connectives. (Contributed by NM, 28-Dec-1992.)
Assertion
Ref Expression
expt ((¬ (𝜑 → ¬ 𝜓) → 𝜒) → (𝜑 → (𝜓𝜒)))

Proof of Theorem expt
StepHypRef Expression
1 pm3.2im 157 . . 3 (𝜑 → (𝜓 → ¬ (𝜑 → ¬ 𝜓)))
21imim1d 82 . 2 (𝜑 → ((¬ (𝜑 → ¬ 𝜓) → 𝜒) → (𝜓𝜒)))
32com12 32 1 ((¬ (𝜑 → ¬ 𝜓) → 𝜒) → (𝜑 → (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by: (None)
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