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Definition df-chj 22653
Description: Define Hilbert lattice join. See chjval 22695 for its value and chjcl 22700 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 22698. (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 22277 . 2  class  vH
2 vx . . 3  set  x
3 vy . . 3  set  y
4 chil 22263 . . . 4  class  ~H
54cpw 3735 . . 3  class  ~P ~H
62cv 1648 . . . . . 6  class  x
73cv 1648 . . . . . 6  class  y
86, 7cun 3254 . . . . 5  class  ( x  u.  y )
9 cort 22274 . . . . 5  class  _|_
108, 9cfv 5387 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 5387 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 6015 . 2  class  ( x  e.  ~P ~H , 
y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y
) ) ) )
131, 12wceq 1649 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  22693
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