Theorem impi 164

Description: An importation inference. (Contributed by NM, 29-Dec-1992.) (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 155	. 2 ⊢ (¬ 𝜒 → (𝜑 → ¬ 𝜓))
3	2	con1i 147	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  166  imp  407