Theorem expt 148

Description: Exportation theorem expressed with primitive connectives. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem expt

Step	Hyp	Ref	Expression
1		pm3.2im 137	. . 3 ⊢ (φ → (ψ → ¬ (φ → ¬ ψ)))
2	1	imim1d 69	. 2 ⊢ (φ → ((¬ (φ → ¬ ψ) → χ) → (ψ → χ)))
3	2	com12 27	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)