Definition df-chj 26204

Description: Define Hilbert lattice join. See chjval 26246 for its value and chjcl 26251 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 26249. (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 25826	. 2 class vH
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		chil 25812	. . . 4 class ~H
5	4	cpw 3997	. . 3 class ~P ~H
6	2	cv 1382	. . . . . 6 class x
7	3	cv 1382	. . . . . 6 class y
8	6, 7	cun 3459	. . . . 5 class ( x u. y )
9		cort 25823	. . . . 5 class _|_
10	8, 9	cfv 5578	. . . 4 class ( _|_ ` ( x u. y ) )
11	10, 9	cfv 5578	. . 3 class ( _|_ ` ( _|_ ` ( x u. y ) ) )
12	2, 3, 5, 5, 11	cmpt2 6283	. 2 class ( x e. ~P ~H , y e. ~P ~H |-> ( _|_ ` ( _|_ ` ( x u. y ) ) ) )
13	1, 12	wceq 1383	1 wff vH = ( x e. ~P ~H , y e. ~P ~H |-> ( _|_ ` ( _|_ ` ( x u. y ) ) ) )

This definition is referenced by:  sshjval  26244