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Definition df-ats 34034
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
StepHypRef Expression
1 catm 34030 . 2 class Atoms
2 vp . . 3 setvar 𝑝
3 cvv 3186 . . 3 class V
42cv 1479 . . . . . 6 class 𝑝
5 cp0 16958 . . . . . 6 class 0.
64, 5cfv 5847 . . . . 5 class (0.‘𝑝)
7 va . . . . . 6 setvar 𝑎
87cv 1479 . . . . 5 class 𝑎
9 ccvr 34029 . . . . . 6 class
104, 9cfv 5847 . . . . 5 class ( ⋖ ‘𝑝)
116, 8, 10wbr 4613 . . . 4 wff (0.‘𝑝)( ⋖ ‘𝑝)𝑎
12 cbs 15781 . . . . 5 class Base
134, 12cfv 5847 . . . 4 class (Base‘𝑝)
1411, 7, 13crab 2911 . . 3 class {𝑎 ∈ (Base‘𝑝) ∣ (0.‘𝑝)( ⋖ ‘𝑝)𝑎}
152, 3, 14cmpt 4673 . 2 class (𝑝 ∈ V ↦ {𝑎 ∈ (Base‘𝑝) ∣ (0.‘𝑝)( ⋖ ‘𝑝)𝑎})
161, 15wceq 1480 1 wff Atoms = (𝑝 ∈ V ↦ {𝑎 ∈ (Base‘𝑝) ∣ (0.‘𝑝)( ⋖ ‘𝑝)𝑎})
Colors of variables: wff setvar class
This definition is referenced by:  pats  34052
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