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Definition df-chj 21883
Description: Define Hilbert lattice join. See chjval 21925 for its value and chjcl 21930 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 21928. (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 21507 . 2  class  vH
2 vx . . 3  set  x
3 vy . . 3  set  y
4 chil 21493 . . . 4  class  ~H
54cpw 3628 . . 3  class  ~P ~H
62cv 1624 . . . . . 6  class  x
73cv 1624 . . . . . 6  class  y
86, 7cun 3153 . . . . 5  class  ( x  u.  y )
9 cort 21504 . . . . 5  class  _|_
108, 9cfv 5223 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 5223 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 5823 . 2  class  ( x  e.  ~P ~H , 
y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y
) ) ) )
131, 12wceq 1625 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  21923
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