Theorem pm2.24d 631

Description: Deduction version of pm2.24 630. (Contributed by NM, 30-Jan-2006.) (Revised by Mario Carneiro, 31-Jan-2015.)

Hypothesis

Ref	Expression
pm2.24d.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
pm2.24d	⊢ (𝜑 → (¬ 𝜓 → 𝜒))

Proof of Theorem pm2.24d

Step	Hyp	Ref	Expression
1		pm2.24d.1	. 2 ⊢ (𝜑 → 𝜓)
2		pm2.24 630	. 2 ⊢ (𝜓 → (¬ 𝜓 → 𝜒))
3	1, 2	syl 14	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-in2 624

This theorem is used by:  pm2.5gdc  878  reldmtpos  6524  nn0o1gt2  12674