Theorem 3bitr3i

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

	Ref	Expression
Hypotheses	3bitr3i.1	|- ( ph <-> ps )
	3bitr3i.2	|- ( ph <-> ch )
	3bitr3i.3	|- ( ps <-> th )
Assertion	3bitr3i	|- ( ch <-> th )

Proof

Step	Hyp	Ref	Expression
1		3bitr3i.1	|- ( ph <-> ps )
2		3bitr3i.2	|- ( ph <-> ch )
3		3bitr3i.3	|- ( ps <-> th )
4	2 1	bitr3i	|- ( ch <-> ps )
5	4 3	bitri	|- ( ch <-> th )