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Definition df-chj 22800
Description: Define Hilbert lattice join. See chjval 22842 for its value and chjcl 22847 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 22845. (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 22424 . 2  class  vH
2 vx . . 3  set  x
3 vy . . 3  set  y
4 chil 22410 . . . 4  class  ~H
54cpw 3791 . . 3  class  ~P ~H
62cv 1651 . . . . . 6  class  x
73cv 1651 . . . . . 6  class  y
86, 7cun 3310 . . . . 5  class  ( x  u.  y )
9 cort 22421 . . . . 5  class  _|_
108, 9cfv 5445 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 5445 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 6074 . 2  class  ( x  e.  ~P ~H , 
y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y
) ) ) )
131, 12wceq 1652 1  wff  vH  =  ( x  e.  ~P ~H ,  y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y ) ) ) )
Colors of variables: wff set class
This definition is referenced by:  sshjval  22840
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