Theorem imbi12d

Description: Deduction joining two equivalences to form equivalence of implications. (Contributed by NM, 16-May-1993)

	Ref	Expression
Hypotheses	imbi12d.1	|- ( ph -> ( ps <-> ch ) )
	imbi12d.2	|- ( ph -> ( th <-> ta ) )
Assertion	imbi12d	|- ( ph -> ( ( ps -> th ) <-> ( ch -> ta ) ) )

Proof

Step	Hyp	Ref	Expression
1		imbi12d.1	|- ( ph -> ( ps <-> ch ) )
2		imbi12d.2	|- ( ph -> ( th <-> ta ) )
3	1	imbi1d	|- ( ph -> ( ( ps -> th ) <-> ( ch -> th ) ) )
4	2	imbi2d	|- ( ph -> ( ( ch -> th ) <-> ( ch -> ta ) ) )
5	3 4	bitrd	|- ( ph -> ( ( ps -> th ) <-> ( ch -> ta ) ) )