Theorem syl5rbb

Description: A syllogism inference from two biconditionals. (Contributed by NM, 1-Aug-1993)

	Ref	Expression
Hypotheses	syl5rbb.1	$$⊢\phi \leftrightarrow \psi$$
	syl5rbb.2	$$⊢\chi \to \left(\psi \leftrightarrow \theta \right)$$
Assertion	syl5rbb	$$⊢\chi \to \left(\theta \leftrightarrow \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		syl5rbb.1	$$⊢\phi \leftrightarrow \psi$$
2		syl5rbb.2	$$⊢\chi \to \left(\psi \leftrightarrow \theta \right)$$
3	1 2	syl5bb	$$⊢\chi \to \left(\phi \leftrightarrow \theta \right)$$
4	3	bicomd	$$⊢\chi \to \left(\theta \leftrightarrow \phi \right)$$