Theorem 3bitrri

Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 4-Aug-2006)

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

Proof

Step	Hyp	Ref	Expression
1		3bitri.1	$$⊢\phi \leftrightarrow \psi$$
2		3bitri.2	$$⊢\psi \leftrightarrow \chi$$
3		3bitri.3	$$⊢\chi \leftrightarrow \theta$$
4	1 2	bitr2i	$$⊢\chi \leftrightarrow \phi$$
5	3 4	bitr3i	$$⊢\theta \leftrightarrow \phi$$