Theorem orbi12d

Description: Deduction joining two equivalences to form equivalence of disjunctions. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Hypotheses	bi12d.1	|- ( ph -> ( ps <-> ch ) )
	bi12d.2	|- ( ph -> ( th <-> ta ) )
Assertion	orbi12d	|- ( ph -> ( ( ps \/ th ) <-> ( ch \/ ta ) ) )

Proof

Step	Hyp	Ref	Expression
1		bi12d.1	|- ( ph -> ( ps <-> ch ) )
2		bi12d.2	|- ( ph -> ( th <-> ta ) )
3	1	orbi1d	|- ( ph -> ( ( ps \/ th ) <-> ( ch \/ th ) ) )
4	2	orbi2d	|- ( ph -> ( ( ch \/ th ) <-> ( ch \/ ta ) ) )
5	3 4	bitrd	|- ( ph -> ( ( ps \/ th ) <-> ( ch \/ ta ) ) )