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	$$⊢\phi \to \neg \psi$$
	sylnib.2	$$⊢\psi \leftrightarrow \chi$$
Assertion	sylnib	$$⊢\phi \to \neg \chi$$

Proof

Step	Hyp	Ref	Expression
1		sylnib.1	$$⊢\phi \to \neg \psi$$
2		sylnib.2	$$⊢\psi \leftrightarrow \chi$$
3	2	biimpri	$$⊢\chi \to \psi$$
4	1 3	nsyl	$$⊢\phi \to \neg \chi$$