Theorem uun2221

Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 30-Dec-2016) (Proof modification is discouraged.) (New usage is discouraged.) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	uun2221.1	|- ( ( ph /\ ph /\ ( ps /\ ph ) ) -> ch )
Assertion	uun2221	|- ( ( ps /\ ph ) -> ch )

Proof

Step	Hyp	Ref	Expression
1		uun2221.1	|- ( ( ph /\ ph /\ ( ps /\ ph ) ) -> ch )
2		3anass	|- ( ( ph /\ ph /\ ( ps /\ ph ) ) <-> ( ph /\ ( ph /\ ( ps /\ ph ) ) ) )
3		anabs5	|- ( ( ph /\ ( ph /\ ( ps /\ ph ) ) ) <-> ( ph /\ ( ps /\ ph ) ) )
4	2 3	bitri	|- ( ( ph /\ ph /\ ( ps /\ ph ) ) <-> ( ph /\ ( ps /\ ph ) ) )
5		ancom	|- ( ( ph /\ ps ) <-> ( ps /\ ph ) )
6	5	anbi2i	|- ( ( ph /\ ( ph /\ ps ) ) <-> ( ph /\ ( ps /\ ph ) ) )
7	4 6	bitr4i	|- ( ( ph /\ ph /\ ( ps /\ ph ) ) <-> ( ph /\ ( ph /\ ps ) ) )
8		anabs5	|- ( ( ph /\ ( ph /\ ps ) ) <-> ( ph /\ ps ) )
9	8 5	bitri	|- ( ( ph /\ ( ph /\ ps ) ) <-> ( ps /\ ph ) )
10	7 9	bitri	|- ( ( ph /\ ph /\ ( ps /\ ph ) ) <-> ( ps /\ ph ) )
11	10	imbi1i	|- ( ( ( ph /\ ph /\ ( ps /\ ph ) ) -> ch ) <-> ( ( ps /\ ph ) -> ch ) )
12	1 11	mpbi	|- ( ( ps /\ ph ) -> ch )