Definition df-chj 24664

Description: Define Hilbert lattice join. See chjval 24706 for its value and chjcl 24711 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 24709. (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 24286	. 2 class vH
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		chil 24272	. . . 4 class ~H
5	4	cpw 3855	. . 3 class ~P ~H
6	2	cv 1368	. . . . . 6 class x
7	3	cv 1368	. . . . . 6 class y
8	6, 7	cun 3321	. . . . 5 class ( x u. y )
9		cort 24283	. . . . 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 6088	. 2 class ( x e. ~P ~H , y e. ~P ~H |-> ( _|_ ` ( _|_ ` ( x u. y ) ) ) )
13	1, 12	wceq 1369	1 wff vH = ( x e. ~P ~H , y e. ~P ~H |-> ( _|_ ` ( _|_ ` ( x u. y ) ) ) )

This definition is referenced by:  sshjval  24704