Theorem expi 141

Description: An exportation inference. (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 28-Nov-2008.)

Hypothesis

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

Assertion

Ref	Expression
expi	⊢ (φ → (ψ → χ))

Proof of Theorem expi

Step	Hyp	Ref	Expression
1		pm3.2im 137	. 2 ⊢ (φ → (ψ → ¬ (φ → ¬ ψ)))
2		expi.1	. 2 ⊢ (¬ (φ → ¬ ψ) → χ)
3	1, 2	syl6 29	1 ⊢ (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:  bi3  179  ex  423