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Definition df-chj 21905
Description: Define Hilbert lattice join. See chjval 21947 for its value and chjcl 21952 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 21950. (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 21529 . 2  class  vH
2 vx . . 3  set  x
3 vy . . 3  set  y
4 chil 21515 . . . 4  class  ~H
54cpw 3638 . . 3  class  ~P ~H
62cv 1631 . . . . . 6  class  x
73cv 1631 . . . . . 6  class  y
86, 7cun 3163 . . . . 5  class  ( x  u.  y )
9 cort 21526 . . . . 5  class  _|_
108, 9cfv 5271 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 5271 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 5876 . 2  class  ( x  e.  ~P ~H , 
y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y
) ) ) )
131, 12wceq 1632 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  21945
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