Definition df-chj 24536

Description: Define Hilbert lattice join. See chjval 24578 for its value and chjcl 24583 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 24581. (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 24158	. 2 class vH
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		chil 24144	. . . 4 class ~H
5	4	cpw 3848	. . 3 class ~P ~H
6	2	cv 1361	. . . . . 6 class x
7	3	cv 1361	. . . . . 6 class y
8	6, 7	cun 3314	. . . . 5 class ( x u. y )
9		cort 24155	. . . . 5 class _|_
10	8, 9	cfv 5406	. . . 4 class ( _|_ ` ( x u. y ) )
11	10, 9	cfv 5406	. . 3 class ( _|_ ` ( _|_ ` ( x u. y ) ) )
12	2, 3, 5, 5, 11	cmpt2 6082	. 2 class ( x e. ~P ~H , y e. ~P ~H |-> ( _|_ ` ( _|_ ` ( x u. y ) ) ) )
13	1, 12	wceq 1362	1 wff vH = ( x e. ~P ~H , y e. ~P ~H |-> ( _|_ ` ( _|_ ` ( x u. y ) ) ) )

This definition is referenced by:  sshjval  24576