Theorem bitr2di

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

	Ref	Expression
Hypotheses	bitr2di.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
	bitr2di.2	$$⊢\chi \leftrightarrow \theta$$
Assertion	bitr2di	$$⊢\phi \to \left(\theta \leftrightarrow \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bitr2di.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		bitr2di.2	$$⊢\chi \leftrightarrow \theta$$
3	1 2	bitrdi	$$⊢\phi \to \left(\psi \leftrightarrow \theta \right)$$
4	3	bicomd	$$⊢\phi \to \left(\theta \leftrightarrow \psi \right)$$