Theorem uunT12p3

Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	uunT12p3.1	|- ( ( ps /\ T. /\ ph ) -> ch )
Assertion	uunT12p3	|- ( ( ph /\ ps ) -> ch )

Proof

Step	Hyp	Ref	Expression
1		uunT12p3.1	|- ( ( ps /\ T. /\ ph ) -> ch )
2		3ancoma	|- ( ( ps /\ T. /\ ph ) <-> ( T. /\ ps /\ ph ) )
3		3anass	|- ( ( T. /\ ps /\ ph ) <-> ( T. /\ ( ps /\ ph ) ) )
4	2 3	bitri	|- ( ( ps /\ T. /\ ph ) <-> ( T. /\ ( ps /\ ph ) ) )
5		truan	|- ( ( T. /\ ( ps /\ ph ) ) <-> ( ps /\ ph ) )
6	4 5	bitri	|- ( ( ps /\ T. /\ ph ) <-> ( ps /\ ph ) )
7		ancom	|- ( ( ph /\ ps ) <-> ( ps /\ ph ) )
8	6 7	bitr4i	|- ( ( ps /\ T. /\ ph ) <-> ( ph /\ ps ) )
9	8 1	sylbir	|- ( ( ph /\ ps ) -> ch )