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Definition df-chj 25890
Description: Define Hilbert lattice join. See chjval 25932 for its value and chjcl 25937 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 25935. (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 25512 . 2  class  vH
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
4 chil 25498 . . . 4  class  ~H
54cpw 4003 . . 3  class  ~P ~H
62cv 1373 . . . . . 6  class  x
73cv 1373 . . . . . 6  class  y
86, 7cun 3467 . . . . 5  class  ( x  u.  y )
9 cort 25509 . . . . 5  class  _|_
108, 9cfv 5579 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 5579 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 6277 . 2  class  ( x  e.  ~P ~H , 
y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y
) ) ) )
131, 12wceq 1374 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  25930
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