Theorem pm2.86d 93

Description: Deduction based on pm2.86 94. (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 28	. 2 ⊢ (φ → (χ → (ψ → θ)))
4	3	com23 72	1 ⊢ (φ → (ψ → (χ → θ)))

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:  pm2.86  94  pm5.74  235  ax12olem6  1932  ax15  2021