Theorem un2122

Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 3-Dec-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	un2122.1	|- ( ( ( ph /\ ps ) /\ ps /\ ps ) -> ch )
Assertion	un2122	|- ( ( ph /\ ps ) -> ch )

Proof

Step	Hyp	Ref	Expression
1		un2122.1	|- ( ( ( ph /\ ps ) /\ ps /\ ps ) -> ch )
2		3anass	|- ( ( ( ph /\ ps ) /\ ps /\ ps ) <-> ( ( ph /\ ps ) /\ ( ps /\ ps ) ) )
3		anandir	|- ( ( ( ph /\ ps ) /\ ps ) <-> ( ( ph /\ ps ) /\ ( ps /\ ps ) ) )
4		ancom	|- ( ( ( ph /\ ps ) /\ ps ) <-> ( ps /\ ( ph /\ ps ) ) )
5		anabs7	|- ( ( ps /\ ( ph /\ ps ) ) <-> ( ph /\ ps ) )
6	4 5	bitri	|- ( ( ( ph /\ ps ) /\ ps ) <-> ( ph /\ ps ) )
7	3 6	bitr3i	|- ( ( ( ph /\ ps ) /\ ( ps /\ ps ) ) <-> ( ph /\ ps ) )
8	2 7	bitri	|- ( ( ( ph /\ ps ) /\ ps /\ ps ) <-> ( ph /\ ps ) )
9	8 1	sylbir	|- ( ( ph /\ ps ) -> ch )