Theorem 3bitri

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

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

Proof

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