Theorem pm2.86iALT 108

Description: Alternate proof of pm2.86i 107 with only three essential steps. (Contributed by NM, 5-Aug-1993.) (Revised by BJ, 19-Jul-2019.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

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

Assertion

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

Proof of Theorem pm2.86iALT

Step	Hyp	Ref	Expression
1		pm2.86i.1	. 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜒))
2		pm2.86 106	. 2 ⊢ (((𝜑 → 𝜓) → (𝜑 → 𝜒)) → (𝜑 → (𝜓 → 𝜒)))
3	1, 2	ax-mp 5	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: (None)