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Definition df-chj 21835
Description: Define Hilbert lattice join. See chjval 21877 for its value and chjcl 21882 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 21880. (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 21459 . 2  class  vH
2 vx . . 3  set  x
3 vy . . 3  set  y
4 chil 21445 . . . 4  class  ~H
54cpw 3585 . . 3  class  ~P ~H
62cv 1618 . . . . . 6  class  x
73cv 1618 . . . . . 6  class  y
86, 7cun 3111 . . . . 5  class  ( x  u.  y )
9 cort 21456 . . . . 5  class  _|_
108, 9cfv 4659 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 4659 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 5780 . 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  21875
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