Definition df-chj 24866

Description: Define Hilbert lattice join. See chjval 24908 for its value and chjcl 24913 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 24911. (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 24488	. 2 class vH
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		chil 24474	. . . 4 class ~H
5	4	cpw 3969	. . 3 class ~P ~H
6	2	cv 1369	. . . . . 6 class x
7	3	cv 1369	. . . . . 6 class y
8	6, 7	cun 3435	. . . . 5 class ( x u. y )
9		cort 24485	. . . . 5 class _|_
10	8, 9	cfv 5527	. . . 4 class ( _|_ ` ( x u. y ) )
11	10, 9	cfv 5527	. . 3 class ( _|_ ` ( _|_ ` ( x u. y ) ) )
12	2, 3, 5, 5, 11	cmpt2 6203	. 2 class ( x e. ~P ~H , y e. ~P ~H |-> ( _|_ ` ( _|_ ` ( x u. y ) ) ) )
13	1, 12	wceq 1370	1 wff vH = ( x e. ~P ~H , y e. ~P ~H |-> ( _|_ ` ( _|_ ` ( x u. y ) ) ) )

This definition is referenced by:  sshjval  24906