Theorem sylbb1

Description: A mixed syllogism inference from two biconditionals. (Contributed by BJ, 21-Apr-2019)

	Ref	Expression
Hypotheses	sylbb1.1	$$⊢\phi \leftrightarrow \psi$$
	sylbb1.2	$$⊢\phi \leftrightarrow \chi$$
Assertion	sylbb1	$$⊢\psi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		sylbb1.1	$$⊢\phi \leftrightarrow \psi$$
2		sylbb1.2	$$⊢\phi \leftrightarrow \chi$$
3	1	biimpri	$$⊢\psi \to \phi$$
4	3 2	sylib	$$⊢\psi \to \chi$$