Theorem uunT12p4

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	uunT12p4.1	|- ( ( ph /\ ps /\ T. ) -> ch )
Assertion	uunT12p4	|- ( ( ph /\ ps ) -> ch )

Proof

Step	Hyp	Ref	Expression
1		uunT12p4.1	|- ( ( ph /\ ps /\ T. ) -> ch )
2		3anrot	|- ( ( T. /\ ph /\ ps ) <-> ( ph /\ ps /\ T. ) )
3		3anass	|- ( ( T. /\ ph /\ ps ) <-> ( T. /\ ( ph /\ ps ) ) )
4	2 3	bitr3i	|- ( ( ph /\ ps /\ T. ) <-> ( T. /\ ( ph /\ ps ) ) )
5		truan	|- ( ( T. /\ ( ph /\ ps ) ) <-> ( ph /\ ps ) )
6	4 5	bitri	|- ( ( ph /\ ps /\ T. ) <-> ( ph /\ ps ) )
7	6 1	sylbir	|- ( ( ph /\ ps ) -> ch )