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Definition df-ats 29457
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
StepHypRef Expression
1 catm 29453 . 2  class  Atoms
2 vp . . 3  set  p
3 cvv 2788 . . 3  class  _V
42cv 1622 . . . . . 6  class  p
5 cp0 14143 . . . . . 6  class  0.
64, 5cfv 5255 . . . . 5  class  ( 0.
`  p )
7 va . . . . . 6  set  a
87cv 1622 . . . . 5  class  a
9 ccvr 29452 . . . . . 6  class  <o
104, 9cfv 5255 . . . . 5  class  (  <o  `  p )
116, 8, 10wbr 4023 . . . 4  wff  ( 0.
`  p ) ( 
<o  `  p ) a
12 cbs 13148 . . . . 5  class  Base
134, 12cfv 5255 . . . 4  class  ( Base `  p )
1411, 7, 13crab 2547 . . 3  class  { a  e.  ( Base `  p
)  |  ( 0.
`  p ) ( 
<o  `  p ) a }
152, 3, 14cmpt 4077 . 2  class  ( p  e.  _V  |->  { a  e.  ( Base `  p
)  |  ( 0.
`  p ) ( 
<o  `  p ) a } )
161, 15wceq 1623 1  wff  Atoms  =  ( p  e.  _V  |->  { a  e.  ( Base `  p )  |  ( 0. `  p ) (  <o  `  p )
a } )
Colors of variables: wff set class
This definition is referenced by:  pats  29475
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