Theorem 3bitr2d

Description: Deduction from transitivity of biconditional. (Contributed by NM, 4-Aug-2006)

	Ref	Expression
Hypotheses	3bitr2d.1	|- ( ph -> ( ps <-> ch ) )
	3bitr2d.2	|- ( ph -> ( th <-> ch ) )
	3bitr2d.3	|- ( ph -> ( th <-> ta ) )
Assertion	3bitr2d	|- ( ph -> ( ps <-> ta ) )

Proof

Step	Hyp	Ref	Expression
1		3bitr2d.1	|- ( ph -> ( ps <-> ch ) )
2		3bitr2d.2	|- ( ph -> ( th <-> ch ) )
3		3bitr2d.3	|- ( ph -> ( th <-> ta ) )
4	1 2	bitr4d	|- ( ph -> ( ps <-> th ) )
5	4 3	bitrd	|- ( ph -> ( ps <-> ta ) )