Theorem 3bitr3i

Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 19-Aug-1993)

	Ref	Expression
Hypotheses	3bitr3i.1	$$⊢\phi \leftrightarrow \psi$$
	3bitr3i.2	$$⊢\phi \leftrightarrow \chi$$
	3bitr3i.3	$$⊢\psi \leftrightarrow \theta$$
Assertion	3bitr3i	$$⊢\chi \leftrightarrow \theta$$

Proof

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