Theorem sylnbir

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

	Ref	Expression
Hypotheses	sylnbir.1	$$⊢\psi \leftrightarrow \phi$$
	sylnbir.2	$$⊢\neg \psi \to \chi$$
Assertion	sylnbir	$$⊢\neg \phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		sylnbir.1	$$⊢\psi \leftrightarrow \phi$$
2		sylnbir.2	$$⊢\neg \psi \to \chi$$
3	1	bicomi	$$⊢\phi \leftrightarrow \psi$$
4	3 2	sylnbi	$$⊢\neg \phi \to \chi$$