Theorem syl6rbb

Description: A syllogism inference from two biconditionals. (Contributed by NM, 5-Aug-1993)

	Ref	Expression
Hypotheses	syl6rbb.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
	syl6rbb.2	$$⊢\chi \leftrightarrow \theta$$
Assertion	syl6rbb	$$⊢\phi \to \left(\theta \leftrightarrow \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		syl6rbb.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		syl6rbb.2	$$⊢\chi \leftrightarrow \theta$$
3	1 2	syl6bb	$$⊢\phi \to \left(\psi \leftrightarrow \theta \right)$$
4	3	bicomd	$$⊢\phi \to \left(\theta \leftrightarrow \psi \right)$$