Theorem expi 647

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 646	. 2 ⊢ (𝜑 → (𝜓 → ¬ (𝜑 → ¬ 𝜓)))
2		expi.1	. 2 ⊢ (¬ (𝜑 → ¬ 𝜓) → 𝜒)
3	1, 2	syl6 33	1 ⊢ (𝜑 → (𝜓 → 𝜒))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 623  ax-in2 624

This theorem is used by:  bj-nn0suc0  16988