Theorem 3bitri

Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 3-Jan-1993)

	Ref	Expression
Hypotheses	3bitri.1	$$⊢\phi \leftrightarrow \psi$$
	3bitri.2	$$⊢\psi \leftrightarrow \chi$$
	3bitri.3	$$⊢\chi \leftrightarrow \theta$$
Assertion	3bitri	$$⊢\phi \leftrightarrow \theta$$

Proof

Step	Hyp	Ref	Expression
1		3bitri.1	$$⊢\phi \leftrightarrow \psi$$
2		3bitri.2	$$⊢\psi \leftrightarrow \chi$$
3		3bitri.3	$$⊢\chi \leftrightarrow \theta$$
4	2 3	bitri	$$⊢\psi \leftrightarrow \theta$$
5	1 4	bitri	$$⊢\phi \leftrightarrow \theta$$