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Definition df-chj 21719
Description: Define Hilbert lattice join. See chjval 21761 for its value and chjcl 21766 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 21764. (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 21343 . 2  class  vH
2 vx . . 3  set  x
3 vy . . 3  set  y
4 chil 21329 . . . 4  class  ~H
54cpw 3530 . . 3  class  ~P ~H
62cv 1618 . . . . . 6  class  x
73cv 1618 . . . . . 6  class  y
86, 7cun 3076 . . . . 5  class  ( x  u.  y )
9 cort 21340 . . . . 5  class  _|_
108, 9cfv 4592 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 4592 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 5712 . 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  21759
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