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Definition df-chj 26949
Description: Define Hilbert lattice join. See chjval 26991 for its value and chjcl 26996 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 26994. (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 26572 . 2  class  vH
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
4 chil 26558 . . . 4  class  ~H
54cpw 3979 . . 3  class  ~P ~H
62cv 1436 . . . . . 6  class  x
73cv 1436 . . . . . 6  class  y
86, 7cun 3434 . . . . 5  class  ( x  u.  y )
9 cort 26569 . . . . 5  class  _|_
108, 9cfv 5598 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 5598 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 6304 . 2  class  ( x  e.  ~P ~H , 
y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y
) ) ) )
131, 12wceq 1437 1  wff  vH  =  ( x  e.  ~P ~H ,  y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y ) ) ) )
Colors of variables: wff setvar class
This definition is referenced by:  sshjval  26989
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