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Definition df-chj 21850
Description: Define Hilbert lattice join. See chjval 21892 for its value and chjcl 21897 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 21895. (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 21474 . 2  class  vH
2 vx . . 3  set  x
3 vy . . 3  set  y
4 chil 21460 . . . 4  class  ~H
54cpw 3599 . . 3  class  ~P ~H
62cv 1618 . . . . . 6  class  x
73cv 1618 . . . . . 6  class  y
86, 7cun 3125 . . . . 5  class  ( x  u.  y )
9 cort 21471 . . . . 5  class  _|_
108, 9cfv 4673 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 4673 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 5794 . 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  21890
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