Definition df-ats 34554

Description: Define the class of poset atoms. (Contributed by NM, 18-Sep-2011.)

Assertion

Ref	Expression
df-ats	|- Atoms = ( p e. _V |-> { a e. ( Base ` p ) | ( 0. ` p ) ( <o ` p ) a } )

Distinct variable group:   p, a

Detailed syntax breakdown of Definition df-ats

Step	Hyp	Ref	Expression
1		catm 34550	. 2 class Atoms
2		vp	. . 3 setvar p
3		cvv 3200	. . 3 class _V
4	2	cv 1482	. . . . . 6 class p
5		cp0 17037	. . . . . 6 class 0.
6	4, 5	cfv 5888	. . . . 5 class ( 0. ` p )
7		va	. . . . . 6 setvar a
8	7	cv 1482	. . . . 5 class a
9		ccvr 34549	. . . . . 6 class <o
10	4, 9	cfv 5888	. . . . 5 class ( <o ` p )
11	6, 8, 10	wbr 4653	. . . 4 wff ( 0. ` p ) ( <o ` p ) a
12		cbs 15857	. . . . 5 class Base
13	4, 12	cfv 5888	. . . 4 class ( Base ` p )
14	11, 7, 13	crab 2916	. . 3 class { a e. ( Base ` p ) | ( 0. ` p ) ( <o ` p ) a }
15	2, 3, 14	cmpt 4729	. 2 class ( p e. _V |-> { a e. ( Base ` p ) | ( 0. ` p ) ( <o ` p ) a } )
16	1, 15	wceq 1483	1 wff Atoms = ( p e. _V |-> { a e. ( Base ` p ) | ( 0. ` p ) ( <o ` p ) a } )

This definition is referenced by:  pats  34572