Theorem uunT12p3 39029

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
uunT12p3.1	|- ( ( ps /\ T. /\ ph ) -> ch )

Assertion

Ref	Expression
uunT12p3	|- ( ( ph /\ ps ) -> ch )

Proof of Theorem uunT12p3

Step	Hyp	Ref	Expression
1		3ancoma 1045	. . . . 5 |- ( ( ps /\ T. /\ ph ) <-> ( T. /\ ps /\ ph ) )
2		3anass 1042	. . . . 5 |- ( ( T. /\ ps /\ ph ) <-> ( T. /\ ( ps /\ ph ) ) )
3	1, 2	bitri 264	. . . 4 |- ( ( ps /\ T. /\ ph ) <-> ( T. /\ ( ps /\ ph ) ) )
4		truan 1501	. . . 4 |- ( ( T. /\ ( ps /\ ph ) ) <-> ( ps /\ ph ) )
5	3, 4	bitri 264	. . 3 |- ( ( ps /\ T. /\ ph ) <-> ( ps /\ ph ) )
6		ancom 466	. . 3 |- ( ( ph /\ ps ) <-> ( ps /\ ph ) )
7	5, 6	bitr4i 267	. 2 |- ( ( ps /\ T. /\ ph ) <-> ( ph /\ ps ) )
8		uunT12p3.1	. 2 |- ( ( ps /\ T. /\ ph ) -> ch )
9	7, 8	sylbir 225	1 |- ( ( ph /\ ps ) -> ch )

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)