Theorem 3bitr3rd

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

	Ref	Expression
Hypotheses	3bitr3d.1	|- ( ph -> ( ps <-> ch ) )
	3bitr3d.2	|- ( ph -> ( ps <-> th ) )
	3bitr3d.3	|- ( ph -> ( ch <-> ta ) )
Assertion	3bitr3rd	|- ( ph -> ( ta <-> th ) )

Proof

Step	Hyp	Ref	Expression
1		3bitr3d.1	|- ( ph -> ( ps <-> ch ) )
2		3bitr3d.2	|- ( ph -> ( ps <-> th ) )
3		3bitr3d.3	|- ( ph -> ( ch <-> ta ) )
4	1 2	bitr3d	|- ( ph -> ( ch <-> th ) )
5	3 4	bitr3d	|- ( ph -> ( ta <-> th ) )