Theorem expt 123

Description: Exportation theorem expressed with primitive connectives.

Assertion

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

Proof of Theorem expt

Step	Hyp	Ref	Expression
1		pm3.2im 107	. . 3 ⊢ (φ → (ψ → ¬ (φ → ¬ ψ)))
2	1	syl4d 28	. 2 ⊢ (φ → ((¬ (φ → ¬ ψ) → χ) → (ψ → χ)))
3	2	com12 13	1 ⊢ ((¬ (φ → ¬ ψ) → χ) → (φ → (ψ → χ)))

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  expi 125  impexp 276

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

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