Theorem pm2.24d 135

Description: Deduction version of pm2.24 101. (Contributed by NM, 30-Jan-2006.)

Hypothesis

Ref	Expression
pm2.24d.1	⊢ (φ → ψ)

Assertion

Ref	Expression
pm2.24d	⊢ (φ → (¬ ψ → χ))

Proof of Theorem pm2.24d

Step	Hyp	Ref	Expression
1		pm2.24d.1	. . 3 ⊢ (φ → ψ)
2	1	a1d 22	. 2 ⊢ (φ → (¬ χ → ψ))
3	2	con1d 116	1 ⊢ (φ → (¬ ψ → χ))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is used by:  pm2.5  144  xpexr  5110