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Definition df-chj 24536
Description: Define Hilbert lattice join. See chjval 24578 for its value and chjcl 24583 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 24581. (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 24158 . 2  class  vH
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
4 chil 24144 . . . 4  class  ~H
54cpw 3848 . . 3  class  ~P ~H
62cv 1361 . . . . . 6  class  x
73cv 1361 . . . . . 6  class  y
86, 7cun 3314 . . . . 5  class  ( x  u.  y )
9 cort 24155 . . . . 5  class  _|_
108, 9cfv 5406 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 5406 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 6082 . 2  class  ( x  e.  ~P ~H , 
y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y
) ) ) )
131, 12wceq 1362 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  24576
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