Theorem orbi2d

Description: Deduction adding a left disjunct to both sides of a logical equivalence. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Hypothesis	bid.1	|- ( ph -> ( ps <-> ch ) )
Assertion	orbi2d	|- ( ph -> ( ( th \/ ps ) <-> ( th \/ ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		bid.1	|- ( ph -> ( ps <-> ch ) )
2	1	imbi2d	|- ( ph -> ( ( -. th -> ps ) <-> ( -. th -> ch ) ) )
3		df-or	|- ( ( th \/ ps ) <-> ( -. th -> ps ) )
4		df-or	|- ( ( th \/ ch ) <-> ( -. th -> ch ) )
5	2 3 4	3bitr4g	|- ( ph -> ( ( th \/ ps ) <-> ( th \/ ch ) ) )