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

Metamath Proof Explorer

Theorem sylnib

Description: A mixed syllogism inference from an implication and a biconditional. (Contributed by Wolf Lammen, 16-Dec-2013)

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

Proof

Step Hyp Ref Expression
1 sylnib.1 ⊢ φ → ¬ ψ
2 sylnib.2 ⊢ ψ ↔ χ
3 2 biimpri ⊢ χ → ψ
4 1 3 nsyl ⊢ φ → ¬ χ