Theorem sylbir

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

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

Proof

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