Theorem impi 140

Description: An importation inference. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 20-Jul-2013.)

Hypothesis

Ref	Expression
impi.1	⊢ (φ → (ψ → χ))

Assertion

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

Proof of Theorem impi

Step	Hyp	Ref	Expression
1		impi.1	. . 3 ⊢ (φ → (ψ → χ))
2	1	con3rr3 128	. 2 ⊢ (¬ χ → (φ → ¬ ψ))
3	2	con1i 121	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:  simprim  142  dfbi1  184  imp  418