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Definition df-chj 22202
Description: Define Hilbert lattice join. See chjval 22244 for its value and chjcl 22249 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 22247. (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 21826 . 2  class  vH
2 vx . . 3  set  x
3 vy . . 3  set  y
4 chil 21812 . . . 4  class  ~H
54cpw 3714 . . 3  class  ~P ~H
62cv 1646 . . . . . 6  class  x
73cv 1646 . . . . . 6  class  y
86, 7cun 3236 . . . . 5  class  ( x  u.  y )
9 cort 21823 . . . . 5  class  _|_
108, 9cfv 5358 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 5358 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 5983 . 2  class  ( x  e.  ~P ~H , 
y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y
) ) ) )
131, 12wceq 1647 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  22242
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