This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem nsyl

Description: A negated syllogism inference. (Contributed by NM, 31-Dec-1993) (Proof shortened by Wolf Lammen, 2-Mar-2013)

Ref Expression
Hypotheses nsyl.1 ⊢ φ → ¬ ψ
nsyl.2 ⊢ χ → ψ
Assertion nsyl ⊢ φ → ¬ χ

Proof

Step Hyp Ref Expression
1 nsyl.1 ⊢ φ → ¬ ψ
2 nsyl.2 ⊢ χ → ψ
3 1 2 nsyl3 ⊢ χ → ¬ φ
4 3 con2i ⊢ φ → ¬ χ