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 → (ψ → χ)) → (¬ (φ → ¬ ψ) → χ))

Proof of Theorem impt

Step	Hyp	Ref	Expression
1		simprim 142	. 2 ⊢ (¬ (φ → ¬ ψ) → ψ)
2		simplim 143	. . 3 ⊢ (¬ (φ → ¬ ψ) → φ)
3	2	imim1i 54	. 2 ⊢ ((φ → (ψ → χ)) → (¬ (φ → ¬ ψ) → (ψ → χ)))
4	1, 3	mpdi 38	1 ⊢ ((φ → (ψ → χ)) → (¬ (φ → ¬ ψ) → χ))

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)