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Definition df-chj 21814
Description: Define Hilbert lattice join. See chjval 21856 for its value and chjcl 21861 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 21859. (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 21438 . 2  class  vH
2 vx . . 3  set  x
3 vy . . 3  set  y
4 chil 21424 . . . 4  class  ~H
54cpw 3566 . . 3  class  ~P ~H
62cv 1618 . . . . . 6  class  x
73cv 1618 . . . . . 6  class  y
86, 7cun 3092 . . . . 5  class  ( x  u.  y )
9 cort 21435 . . . . 5  class  _|_
108, 9cfv 4638 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 4638 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 5759 . 2  class  ( x  e.  ~P ~H , 
y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y
) ) ) )
131, 12wceq 1619 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  21854
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