Theorem bitr3id

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

	Ref	Expression
Hypotheses	bitr3id.1	$$⊢\psi \leftrightarrow \phi$$
	bitr3id.2	$$⊢\chi \to \left(\psi \leftrightarrow \theta \right)$$
Assertion	bitr3id	$$⊢\chi \to \left(\phi \leftrightarrow \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		bitr3id.1	$$⊢\psi \leftrightarrow \phi$$
2		bitr3id.2	$$⊢\chi \to \left(\psi \leftrightarrow \theta \right)$$
3	1	bicomi	$$⊢\phi \leftrightarrow \psi$$
4	3 2	syl5bb	$$⊢\chi \to \left(\phi \leftrightarrow \theta \right)$$