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Theorem impt 181
Description: Importation theorem pm3.1 989 (closed form of imp 410) expressed with primitive connectives. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 20-Jul-2013.)
Assertion
Ref Expression
impt ((𝜑 → (𝜓𝜒)) → (¬ (𝜑 → ¬ 𝜓) → 𝜒))

Proof of Theorem impt
StepHypRef Expression
1 simprim 169 . 2 (¬ (𝜑 → ¬ 𝜓) → 𝜓)
2 simplim 170 . . 3 (¬ (𝜑 → ¬ 𝜓) → 𝜑)
32imim1i 63 . 2 ((𝜑 → (𝜓𝜒)) → (¬ (𝜑 → ¬ 𝜓) → (𝜓𝜒)))
41, 3mpdi 45 1 ((𝜑 → (𝜓𝜒)) → (¬ (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: (None)
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