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Definition df-at 28369
Description: Define the set of atoms in a Hilbert lattice. An atom is a nonzero element of a lattice such that anything less than it is zero, i.e. it is the smallest nonzero element of the lattice. Definition of atom in [Kalmbach] p. 15. See ela 28370 and elat2 28371 for membership relations. (Contributed by NM, 14-Aug-2002.) (New usage is discouraged.)
Assertion
Ref Expression
df-at HAtoms = {𝑥C ∣ 0 𝑥}

Detailed syntax breakdown of Definition df-at
StepHypRef Expression
1 cat 26994 . 2 class HAtoms
2 c0h 26964 . . . 4 class 0
3 vx . . . . 5 setvar 𝑥
43cv 1473 . . . 4 class 𝑥
5 ccv 26993 . . . 4 class
62, 4, 5wbr 4481 . . 3 wff 0 𝑥
7 cch 26958 . . 3 class C
86, 3, 7crab 2804 . 2 class {𝑥C ∣ 0 𝑥}
91, 8wceq 1474 1 wff HAtoms = {𝑥C ∣ 0 𝑥}
Colors of variables: wff setvar class
This definition is referenced by:  ela  28370  atssch  28374
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