Theorem 3bitr4i

Description: A chained inference from transitive law for logical equivalence. This inference is frequently used to apply a definition to both sides of a logical equivalence. (Contributed by NM, 3-Jan-1993)

	Ref	Expression
Hypotheses	3bitr4i.1	|- ( ph <-> ps )
	3bitr4i.2	|- ( ch <-> ph )
	3bitr4i.3	|- ( th <-> ps )
Assertion	3bitr4i	|- ( ch <-> th )

Proof

Step	Hyp	Ref	Expression
1		3bitr4i.1	|- ( ph <-> ps )
2		3bitr4i.2	|- ( ch <-> ph )
3		3bitr4i.3	|- ( th <-> ps )
4	1 3	bitr4i	|- ( ph <-> th )
5	2 4	bitri	|- ( ch <-> th )