Definition df-chj 28169

Description: Define Hilbert lattice join. See chjval 28211 for its value and chjcl 28216 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 28214. (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 27790	. 2 class vH
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		chil 27776	. . . 4 class ~H
5	4	cpw 4158	. . 3 class ~P ~H
6	2	cv 1482	. . . . . 6 class x
7	3	cv 1482	. . . . . 6 class y
8	6, 7	cun 3572	. . . . 5 class ( x u. y )
9		cort 27787	. . . . 5 class _|_
10	8, 9	cfv 5888	. . . 4 class ( _|_ ` ( x u. y ) )
11	10, 9	cfv 5888	. . 3 class ( _|_ ` ( _|_ ` ( x u. y ) ) )
12	2, 3, 5, 5, 11	cmpt2 6652	. 2 class ( x e. ~P ~H , y e. ~P ~H |-> ( _|_ ` ( _|_ ` ( x u. y ) ) ) )
13	1, 12	wceq 1483	1 wff vH = ( x e. ~P ~H , y e. ~P ~H |-> ( _|_ ` ( _|_ ` ( x u. y ) ) ) )

This definition is referenced by:  sshjval  28209