Theorem pm2.86i 92

Description: Inference based on pm2.86 94. (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 15	. 2 ⊢ (ψ → (φ → χ))
4	3	com12 27	1 ⊢ (φ → (ψ → χ))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by: (None)