Theorem impt 122

Description: Importation theorem expressed with primitive connectives.

Assertion

Ref	Expression
impt	⊢ ((φ → (ψ → χ)) → (¬ (φ → ¬ ψ) → χ))

Proof of Theorem impt

Step	Hyp	Ref	Expression
1		con3 86	. . . 4 ⊢ ((ψ → χ) → (¬ χ → ¬ ψ))
2	1	syl3 18	. . 3 ⊢ ((φ → (ψ → χ)) → (φ → (¬ χ → ¬ ψ)))
3	2	com23 32	. 2 ⊢ ((φ → (ψ → χ)) → (¬ χ → (φ → ¬ ψ)))
4	3	con1d 85	1 ⊢ ((φ → (ψ → χ)) → (¬ (φ → ¬ ψ) → χ))

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  impi 124  impexp 276

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

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