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Definition df-chj 22804
Description: Define Hilbert lattice join. See chjval 22846 for its value and chjcl 22851 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 22849. (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 22428 . 2  class  vH
2 vx . . 3  set  x
3 vy . . 3  set  y
4 chil 22414 . . . 4  class  ~H
54cpw 3791 . . 3  class  ~P ~H
62cv 1651 . . . . . 6  class  x
73cv 1651 . . . . . 6  class  y
86, 7cun 3310 . . . . 5  class  ( x  u.  y )
9 cort 22425 . . . . 5  class  _|_
108, 9cfv 5446 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 5446 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 6075 . 2  class  ( x  e.  ~P ~H , 
y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y
) ) ) )
131, 12wceq 1652 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  22844
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