Definition df-chj 22765

Description: Define Hilbert lattice join. See chjval 22807 for its value and chjcl 22812 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 22810. (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

Step	Hyp	Ref	Expression
1		chj 22389	. 2 class vH
2		vx	. . 3 set x
3		vy	. . 3 set y
4		chil 22375	. . . 4 class ~H
5	4	cpw 3759	. . 3 class ~P ~H
6	2	cv 1648	. . . . . 6 class x
7	3	cv 1648	. . . . . 6 class y
8	6, 7	cun 3278	. . . . 5 class ( x u. y )
9		cort 22386	. . . . 5 class _|_
10	8, 9	cfv 5413	. . . 4 class ( _|_ ` ( x u. y ) )
11	10, 9	cfv 5413	. . 3 class ( _|_ ` ( _|_ ` ( x u. y ) ) )
12	2, 3, 5, 5, 11	cmpt2 6042	. 2 class ( x e. ~P ~H , y e. ~P ~H |-> ( _|_ ` ( _|_ ` ( x u. y ) ) ) )
13	1, 12	wceq 1649	1 wff vH = ( x e. ~P ~H , y e. ~P ~H |-> ( _|_ ` ( _|_ ` ( x u. y ) ) ) )

This definition is referenced by:  sshjval  22805