Theorem syl6bb

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

	Ref	Expression
Hypotheses	syl6bb.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
	syl6bb.2	$$⊢\chi \leftrightarrow \theta$$
Assertion	syl6bb	$$⊢\phi \to \left(\psi \leftrightarrow \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		syl6bb.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		syl6bb.2	$$⊢\chi \leftrightarrow \theta$$
3	2	a1i	$$⊢\phi \to \left(\chi \leftrightarrow \theta \right)$$
4	1 3	bitrd	$$⊢\phi \to \left(\psi \leftrightarrow \theta \right)$$