Theorem sylib

Description: A mixed syllogism inference from an implication and a biconditional. (Contributed by NM, 3-Jan-1993)

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

Proof

Step	Hyp	Ref	Expression
1		sylib.1	$$⊢\phi \to \psi$$
2		sylib.2	$$⊢\psi \leftrightarrow \chi$$
3	2	biimpi	$$⊢\psi \to \chi$$
4	1 3	syl	$$⊢\phi \to \chi$$