Theorem uunTT1p1 39021

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.)

Hypothesis

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

Assertion

Ref	Expression
uunTT1p1	|- ( ph -> ps )

Proof of Theorem uunTT1p1

Step	Hyp	Ref	Expression
1		3ancomb 1047	. . . 4 |- ( ( T. /\ ph /\ T. ) <-> ( T. /\ T. /\ ph ) )
2		3anass 1042	. . . 4 |- ( ( T. /\ T. /\ ph ) <-> ( T. /\ ( T. /\ ph ) ) )
3		anabs5 851	. . . 4 |- ( ( T. /\ ( T. /\ ph ) ) <-> ( T. /\ ph ) )
4	1, 2, 3	3bitri 286	. . 3 |- ( ( T. /\ ph /\ T. ) <-> ( T. /\ ph ) )
5		truan 1501	. . 3 |- ( ( T. /\ ph ) <-> ph )
6	4, 5	bitri 264	. 2 |- ( ( T. /\ ph /\ T. ) <-> ph )
7		uunTT1p1.1	. 2 |- ( ( T. /\ ph /\ T. ) -> ps )
8	6, 7	sylbir 225	1 |- ( ph -> ps )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037   T. wtru 1484

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039  df-tru 1486

This theorem is referenced by: (None)