Theorem 3bitr4d

Description: Deduction from transitivity of biconditional. Useful for converting conditional definitions in a formula. (Contributed by NM, 18-Oct-1995)

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

Proof

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