Theorem 3bitr3ri

Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Hypotheses	3bitr3i.1	|- ( ph <-> ps )
	3bitr3i.2	|- ( ph <-> ch )
	3bitr3i.3	|- ( ps <-> th )
Assertion	3bitr3ri	|- ( th <-> ch )

Proof

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