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Definition df-chj 21889
Description: Define Hilbert lattice join. See chjval 21931 for its value and chjcl 21936 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 21934. (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 21513 . 2  class  vH
2 vx . . 3  set  x
3 vy . . 3  set  y
4 chil 21499 . . . 4  class  ~H
54cpw 3625 . . 3  class  ~P ~H
62cv 1622 . . . . . 6  class  x
73cv 1622 . . . . . 6  class  y
86, 7cun 3150 . . . . 5  class  ( x  u.  y )
9 cort 21510 . . . . 5  class  _|_
108, 9cfv 5255 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 5255 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 5860 . 2  class  ( x  e.  ~P ~H , 
y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y
) ) ) )
131, 12wceq 1623 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  21929
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