Definition df-ats 33572

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

Assertion

Ref	Expression
df-ats	⊢ Atoms = (𝑝 ∈ V ↦ {𝑎 ∈ (Base‘𝑝) ∣ (0.‘𝑝)( ⋖ ‘𝑝)𝑎})

Distinct variable group:   𝑝,𝑎

Detailed syntax breakdown of Definition df-ats

Step	Hyp	Ref	Expression
1		catm 33568	. 2 class Atoms
2		vp	. . 3 setvar 𝑝
3		cvv 3173	. . 3 class V
4	2	cv 1474	. . . . . 6 class 𝑝
5		cp0 16860	. . . . . 6 class 0.
6	4, 5	cfv 5804	. . . . 5 class (0.‘𝑝)
7		va	. . . . . 6 setvar 𝑎
8	7	cv 1474	. . . . 5 class 𝑎
9		ccvr 33567	. . . . . 6 class ⋖
10	4, 9	cfv 5804	. . . . 5 class ( ⋖ ‘𝑝)
11	6, 8, 10	wbr 4583	. . . 4 wff (0.‘𝑝)( ⋖ ‘𝑝)𝑎
12		cbs 15695	. . . . 5 class Base
13	4, 12	cfv 5804	. . . 4 class (Base‘𝑝)
14	11, 7, 13	crab 2900	. . 3 class {𝑎 ∈ (Base‘𝑝) ∣ (0.‘𝑝)( ⋖ ‘𝑝)𝑎}
15	2, 3, 14	cmpt 4643	. 2 class (𝑝 ∈ V ↦ {𝑎 ∈ (Base‘𝑝) ∣ (0.‘𝑝)( ⋖ ‘𝑝)𝑎})
16	1, 15	wceq 1475	1 wff Atoms = (𝑝 ∈ V ↦ {𝑎 ∈ (Base‘𝑝) ∣ (0.‘𝑝)( ⋖ ‘𝑝)𝑎})

This definition is referenced by:  pats  33590