Theorem sylbb2

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

	Ref	Expression
Hypotheses	sylbb2.1	$$⊢\phi \leftrightarrow \psi$$
	sylbb2.2	$$⊢\chi \leftrightarrow \psi$$
Assertion	sylbb2	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		sylbb2.1	$$⊢\phi \leftrightarrow \psi$$
2		sylbb2.2	$$⊢\chi \leftrightarrow \psi$$
3	2	biimpri	$$⊢\psi \to \chi$$
4	1 3	sylbi	$$⊢\phi \to \chi$$