Theorem expi 125

Description: An exportation inference.

Hypothesis

Ref	Expression
expi.1	⊢ (¬ (φ → ¬ ψ) → χ)

Assertion

Ref	Expression
expi	⊢ (φ → (ψ → χ))

Proof of Theorem expi

Step	Hyp	Ref	Expression
1		expi.1	. 2 ⊢ (¬ (φ → ¬ ψ) → χ)
2		expt 123	. 2 ⊢ ((¬ (φ → ¬ ψ) → χ) → (φ → (ψ → χ)))
3	1, 2	ax-mp 6	1 ⊢ (φ → (ψ → χ))

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  bi3 132  pm3.2 232  exp 291  fr2nr 2177  fr3nr 2178

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

metamath.org