Metamath Proof Explorer


Theorem nsyl2

Description: A negated syllogism inference. (Contributed by NM, 26-Jun-1994) (Proof shortened by Wolf Lammen, 14-Nov-2023)

Ref Expression
Hypotheses nsyl2.1 φ¬ψ
nsyl2.2 ¬χψ
Assertion nsyl2 φχ

Proof

Step Hyp Ref Expression
1 nsyl2.1 φ¬ψ
2 nsyl2.2 ¬χψ
3 1 2 nsyl3 ¬χ¬φ
4 3 con4i φχ