Theorem bitr4di

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

	Ref	Expression
Hypotheses	bitr4di.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
	bitr4di.2	$$⊢\theta \leftrightarrow \chi$$
Assertion	bitr4di	$$⊢\phi \to \left(\psi \leftrightarrow \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		bitr4di.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		bitr4di.2	$$⊢\theta \leftrightarrow \chi$$
3	2	bicomi	$$⊢\chi \leftrightarrow \theta$$
4	1 3	bitrdi	$$⊢\phi \to \left(\psi \leftrightarrow \theta \right)$$