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Definition df-chj 21891
Description: Define Hilbert lattice join. See chjval 21933 for its value and chjcl 21938 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 21936. (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 21515 . 2  class  vH
2 vx . . 3  set  x
3 vy . . 3  set  y
4 chil 21501 . . . 4  class  ~H
54cpw 3627 . . 3  class  ~P ~H
62cv 1624 . . . . . 6  class  x
73cv 1624 . . . . . 6  class  y
86, 7cun 3152 . . . . 5  class  ( x  u.  y )
9 cort 21512 . . . . 5  class  _|_
108, 9cfv 5257 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 5257 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 5862 . 2  class  ( x  e.  ~P ~H , 
y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y
) ) ) )
131, 12wceq 1625 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  21931
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