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Theorem impi 158
Description: An importation inference. (Contributed by NM, 29-Dec-1992.) (Proof shortened by Wolf Lammen, 20-Jul-2013.)
Hypothesis
Ref Expression
impi.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
impi (¬ (𝜑 → ¬ 𝜓) → 𝜒)

Proof of Theorem impi
StepHypRef Expression
1 impi.1 . . 3 (𝜑 → (𝜓𝜒))
21con3rr3 149 . 2 𝜒 → (𝜑 → ¬ 𝜓))
32con1i 142 1 (¬ (𝜑 → ¬ 𝜓) → 𝜒)
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:  simprim  160  dfbi1  201  imp  443
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