Theorem bitri

Description: An inference from transitive law for logical equivalence. (Contributed by NM, 3-Jan-1993) (Proof shortened by Wolf Lammen, 13-Oct-2012)

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

Proof

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