Theorem 3bitrri

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

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

Proof

Step	Hyp	Ref	Expression
1		3bitri.1	|- ( ph <-> ps )
2		3bitri.2	|- ( ps <-> ch )
3		3bitri.3	|- ( ch <-> th )
4	1 2	bitr2i	|- ( ch <-> ph )
5	3 4	bitr3i	|- ( th <-> ph )