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Definition df-at 25893
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 25894 and elat2 25895 for membership relations. (Contributed by NM, 14-Aug-2002.) (New usage is discouraged.)
Assertion
Ref Expression
df-at  |- HAtoms  =  {
x  e.  CH  |  0H  <oH  x }

Detailed syntax breakdown of Definition df-at
StepHypRef Expression
1 cat 24518 . 2  class HAtoms
2 c0h 24488 . . . 4  class  0H
3 vx . . . . 5  setvar  x
43cv 1369 . . . 4  class  x
5 ccv 24517 . . . 4  class  <oH
62, 4, 5wbr 4399 . . 3  wff  0H  <oH  x
7 cch 24482 . . 3  class  CH
86, 3, 7crab 2802 . 2  class  { x  e.  CH  |  0H  <oH  x }
91, 8wceq 1370 1  wff HAtoms  =  {
x  e.  CH  |  0H  <oH  x }
Colors of variables: wff setvar class
This definition is referenced by:  ela  25894  atssch  25898
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