Theorem bitrdi

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

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

Proof

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