Theorem nsyl3 104

Description: A negated syllogism inference.

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	con2i 89	. 2 ⊢ (ψ → ¬ φ)
4	1, 3	syl 12	1 ⊢ (χ → ¬ φ)

Syntax hints:  ¬ wn 1   → wi 2

This theorem is referenced by:  sdomirr 3314  sucprcreg 3451  cardnn 3631  add20 4329

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

metamath.org