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Definition df-chj 26963
Description: Define Hilbert lattice join. See chjval 27005 for its value and chjcl 27010 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 27008. (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 26586 . 2  class  vH
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
4 chil 26572 . . . 4  class  ~H
54cpw 3951 . . 3  class  ~P ~H
62cv 1443 . . . . . 6  class  x
73cv 1443 . . . . . 6  class  y
86, 7cun 3402 . . . . 5  class  ( x  u.  y )
9 cort 26583 . . . . 5  class  _|_
108, 9cfv 5582 . . . 4  class  ( _|_ `  ( x  u.  y
) )
1110, 9cfv 5582 . . 3  class  ( _|_ `  ( _|_ `  (
x  u.  y ) ) )
122, 3, 5, 5, 11cmpt2 6292 . 2  class  ( x  e.  ~P ~H , 
y  e.  ~P ~H  |->  ( _|_ `  ( _|_ `  ( x  u.  y
) ) ) )
131, 12wceq 1444 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  27003
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