Theorem syl6bbr

Description: A syllogism inference from two biconditionals. (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Hypotheses	syl6bbr.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
	syl6bbr.2	$$⊢\theta \leftrightarrow \chi$$
Assertion	syl6bbr	$$⊢\phi \to \left(\psi \leftrightarrow \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		syl6bbr.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		syl6bbr.2	$$⊢\theta \leftrightarrow \chi$$
3	2	bicomi	$$⊢\chi \leftrightarrow \theta$$
4	1 3	syl6bb	$$⊢\phi \to \left(\psi \leftrightarrow \theta \right)$$