Theorem 3bitrd

Description: Deduction from transitivity of biconditional. (Contributed by NM, 13-Aug-1999)

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

Proof

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