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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 ⊢ ¬ χ → ψ
Assertion nsyl2 ⊢ φ → χ

Proof

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