Theorem uunTT1p1

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	uunTT1p1.1	|- ( ( T. /\ ph /\ T. ) -> ps )
Assertion	uunTT1p1	|- ( ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		uunTT1p1.1	|- ( ( T. /\ ph /\ T. ) -> ps )
2		3ancomb	|- ( ( T. /\ ph /\ T. ) <-> ( T. /\ T. /\ ph ) )
3		3anass	|- ( ( T. /\ T. /\ ph ) <-> ( T. /\ ( T. /\ ph ) ) )
4		anabs5	|- ( ( T. /\ ( T. /\ ph ) ) <-> ( T. /\ ph ) )
5	2 3 4	3bitri	|- ( ( T. /\ ph /\ T. ) <-> ( T. /\ ph ) )
6		truan	|- ( ( T. /\ ph ) <-> ph )
7	5 6	bitri	|- ( ( T. /\ ph /\ T. ) <-> ph )
8	7 1	sylbir	|- ( ph -> ps )