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Definition df-chj 21884
Description: Define Hilbert lattice join. See chjval 21926 for its value and chjcl 21931 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 21929. (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 21508 . 2  class  vH
2 vx . . 3  set  x
3 vy . . 3  set  y
4 chil 21494 . . . 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 21505 . . . . 5  class  _|_
108, 9cfv 5220 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 5220 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 5821 . 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  21924
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