Definition df-chj 25890

Description: Define Hilbert lattice join. See chjval 25932 for its value and chjcl 25937 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 25935. (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 25512	. 2 class vH
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		chil 25498	. . . 4 class ~H
5	4	cpw 4003	. . 3 class ~P ~H
6	2	cv 1373	. . . . . 6 class x
7	3	cv 1373	. . . . . 6 class y
8	6, 7	cun 3467	. . . . 5 class ( x u. y )
9		cort 25509	. . . . 5 class _|_
10	8, 9	cfv 5579	. . . 4 class ( _|_ ` ( x u. y ) )
11	10, 9	cfv 5579	. . 3 class ( _|_ ` ( _|_ ` ( x u. y ) ) )
12	2, 3, 5, 5, 11	cmpt2 6277	. 2 class ( x e. ~P ~H , y e. ~P ~H |-> ( _|_ ` ( _|_ ` ( x u. y ) ) ) )
13	1, 12	wceq 1374	1 wff vH = ( x e. ~P ~H , y e. ~P ~H |-> ( _|_ ` ( _|_ ` ( x u. y ) ) ) )

This definition is referenced by:  sshjval  25930