Theorem pm2.86d 99

Description: Deduction based on pm2.86 100. (Contributed by NM, 29-Jun-1995.) (Proof shortened by Wolf Lammen, 3-Apr-2013.)

Hypothesis

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

Assertion

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

Proof of Theorem pm2.86d

Step	Hyp	Ref	Expression
1		ax-1 6	. . 3 ⊢ (𝜒 → (𝜓 → 𝜒))
2		pm2.86d.1	. . 3 ⊢ (𝜑 → ((𝜓 → 𝜒) → (𝜓 → 𝜃)))
3	1, 2	syl5 32	. 2 ⊢ (𝜑 → (𝜒 → (𝜓 → 𝜃)))
4	3	com23 78	1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Syntax hints:   → wi 4

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

This theorem is referenced by:  pm2.86  100  pm5.74  178