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Definition df-chj 24866
Description: Define Hilbert lattice join. See chjval 24908 for its value and chjcl 24913 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 24911. (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 24488 . 2  class  vH
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
4 chil 24474 . . . 4  class  ~H
54cpw 3969 . . 3  class  ~P ~H
62cv 1369 . . . . . 6  class  x
73cv 1369 . . . . . 6  class  y
86, 7cun 3435 . . . . 5  class  ( x  u.  y )
9 cort 24485 . . . . 5  class  _|_
108, 9cfv 5527 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 5527 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 6203 . 2  class  ( x  e.  ~P ~H , 
y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y
) ) ) )
131, 12wceq 1370 1  wff  vH  =  ( x  e.  ~P ~H ,  y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y ) ) ) )
Colors of variables: wff setvar class
This definition is referenced by:  sshjval  24906
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