Theorem bitr2id

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

	Ref	Expression
Hypotheses	bitr2id.1	$$⊢\phi \leftrightarrow \psi$$
	bitr2id.2	$$⊢\chi \to \left(\psi \leftrightarrow \theta \right)$$
Assertion	bitr2id	$$⊢\chi \to \left(\theta \leftrightarrow \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bitr2id.1	$$⊢\phi \leftrightarrow \psi$$
2		bitr2id.2	$$⊢\chi \to \left(\psi \leftrightarrow \theta \right)$$
3	1 2	bitrid	$$⊢\chi \to \left(\phi \leftrightarrow \theta \right)$$
4	3	bicomd	$$⊢\chi \to \left(\theta \leftrightarrow \phi \right)$$