Theorem 3imtr4d

Description: More general version of 3imtr4i . Useful for converting conditional definitions in a formula. (Contributed by NM, 26-Oct-1995)

	Ref	Expression
Hypotheses	3imtr4d.1	|- ( ph -> ( ps -> ch ) )
	3imtr4d.2	|- ( ph -> ( th <-> ps ) )
	3imtr4d.3	|- ( ph -> ( ta <-> ch ) )
Assertion	3imtr4d	|- ( ph -> ( th -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		3imtr4d.1	|- ( ph -> ( ps -> ch ) )
2		3imtr4d.2	|- ( ph -> ( th <-> ps ) )
3		3imtr4d.3	|- ( ph -> ( ta <-> ch ) )
4	1 3	sylibrd	|- ( ph -> ( ps -> ta ) )
5	2 4	sylbid	|- ( ph -> ( th -> ta ) )