Theorem 3imtr3d

Description: More general version of 3imtr3i . Useful for converting conditional definitions in a formula. (Contributed by NM, 8-Apr-1996)

	Ref	Expression
Hypotheses	3imtr3d.1	|- ( ph -> ( ps -> ch ) )
	3imtr3d.2	|- ( ph -> ( ps <-> th ) )
	3imtr3d.3	|- ( ph -> ( ch <-> ta ) )
Assertion	3imtr3d	|- ( ph -> ( th -> ta ) )

Proof

Step	Hyp	Ref	Expression
1		3imtr3d.1	|- ( ph -> ( ps -> ch ) )
2		3imtr3d.2	|- ( ph -> ( ps <-> th ) )
3		3imtr3d.3	|- ( ph -> ( ch <-> ta ) )
4	1 3	sylibd	|- ( ph -> ( ps -> ta ) )
5	2 4	sylbird	|- ( ph -> ( th -> ta ) )