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Definition df-chj 24664
Description: Define Hilbert lattice join. See chjval 24706 for its value and chjcl 24711 for its closure law. Note that we define it over all Hilbert space subsets to allow proving more general theorems. Even for general subsets the join belongs to  CH; see sshjcl 24709. (Contributed by NM, 1-Nov-2000.) (New usage is discouraged.)
Assertion
Ref Expression
df-chj  |-  vH  =  ( x  e.  ~P ~H ,  y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y ) ) ) )
Distinct variable group:    x, y

Detailed syntax breakdown of Definition df-chj
StepHypRef Expression
1 chj 24286 . 2  class  vH
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
4 chil 24272 . . . 4  class  ~H
54cpw 3855 . . 3  class  ~P ~H
62cv 1368 . . . . . 6  class  x
73cv 1368 . . . . . 6  class  y
86, 7cun 3321 . . . . 5  class  ( x  u.  y )
9 cort 24283 . . . . 5  class  _|_
108, 9cfv 5413 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 5413 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 6088 . 2  class  ( x  e.  ~P ~H , 
y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y
) ) ) )
131, 12wceq 1369 1  wff  vH  =  ( x  e.  ~P ~H ,  y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y ) ) ) )
Colors of variables: wff setvar class
This definition is referenced by:  sshjval  24704
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