Theorem nsyl4 134

Description: A negated syllogism inference. (Contributed by NM, 15-Feb-1996.)

Hypotheses

Ref	Expression
nsyl4.1	⊢ (φ → ψ)
nsyl4.2	⊢ (¬ φ → χ)

Assertion

Ref	Expression
nsyl4	⊢ (¬ χ → ψ)

Proof of Theorem nsyl4

Step	Hyp	Ref	Expression
1		nsyl4.2	. . 3 ⊢ (¬ φ → χ)
2	1	con1i 121	. 2 ⊢ (¬ χ → φ)
3		nsyl4.1	. 2 ⊢ (φ → ψ)
4	2, 3	syl 15	1 ⊢ (¬ χ → ψ)

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:  pm5.55  867  ax6o  1750  hbimdOLD  1816  naecoms  1948  ax6  2147  ax467  2169  ax467to7  2172  naecoms-o  2178  nfunsn  5354