Theorem nsyl3 111

Description: A negated syllogism inference. (Contributed by NM, 1-Dec-1995.)

Hypotheses

Ref	Expression
nsyl3.1	⊢ (φ → ¬ ψ)
nsyl3.2	⊢ (χ → ψ)

Assertion

Ref	Expression
nsyl3	⊢ (χ → ¬ φ)

Proof of Theorem nsyl3

Step	Hyp	Ref	Expression
1		nsyl3.2	. 2 ⊢ (χ → ψ)
2		nsyl3.1	. . 3 ⊢ (φ → ¬ ψ)
3	2	a1i 10	. 2 ⊢ (χ → (φ → ¬ ψ))
4	1, 3	mt2d 109	1 ⊢ (χ → ¬ φ)

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  con2i  112  nsyl  113  ax9  1949  cesare  2307  cesaro  2311