Theorem pm2.86i 98

Description: Inference based on pm2.86 100. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 3-Apr-2013.)

Hypothesis

Ref	Expression
pm2.86i.1	⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜒))

Assertion

Ref	Expression
pm2.86i	⊢ (𝜑 → (𝜓 → 𝜒))

Proof of Theorem pm2.86i

Step	Hyp	Ref	Expression
1		ax-1 6	. . 3 ⊢ (𝜓 → (𝜑 → 𝜓))
2		pm2.86i.1	. . 3 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜒))
3	1, 2	syl 14	. 2 ⊢ (𝜓 → (𝜑 → 𝜒))
4	3	com12 30	1 ⊢ (𝜑 → (𝜓 → 𝜒))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  nfrimi  1518  cbv1  1738  cbv1v  1740