Theorem orbi1d

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

	Ref	Expression
Hypothesis	bid.1	|- ( ph -> ( ps <-> ch ) )
Assertion	orbi1d	|- ( ph -> ( ( ps \/ th ) <-> ( ch \/ th ) ) )

Proof

Step	Hyp	Ref	Expression
1		bid.1	|- ( ph -> ( ps <-> ch ) )
2	1	orbi2d	|- ( ph -> ( ( th \/ ps ) <-> ( th \/ ch ) ) )
3		orcom	|- ( ( ps \/ th ) <-> ( th \/ ps ) )
4		orcom	|- ( ( ch \/ th ) <-> ( th \/ ch ) )
5	2 3 4	3bitr4g	|- ( ph -> ( ( ps \/ th ) <-> ( ch \/ th ) ) )