Theorem 3bitr4rd

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

	Ref	Expression
Hypotheses	3bitr4d.1	|- ( ph -> ( ps <-> ch ) )
	3bitr4d.2	|- ( ph -> ( th <-> ps ) )
	3bitr4d.3	|- ( ph -> ( ta <-> ch ) )
Assertion	3bitr4rd	|- ( ph -> ( ta <-> th ) )

Proof

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