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Theorem impt 149
Description: Importation theorem 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 142 . 2 (¬ (φ → ¬ ψ) → ψ)
2 simplim 143 . . 3 (¬ (φ → ¬ ψ) → φ)
32imim1i 54 . 2 ((φ → (ψχ)) → (¬ (φ → ¬ ψ) → (ψχ)))
41, 3mpdi 38 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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