Theorem sylbb

Description: A mixed syllogism inference from two biconditionals. (Contributed by BJ, 30-Mar-2019)

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

Proof

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