Definition df-dom 7570

Description: Define the dominance relation. For an alternate definition see dfdom2 7593. Compare Definition of [Enderton] p. 145. Typical textbook definitions are derived as brdom 7580 and domen 7581. (Contributed by NM, 28-Mar-1998.)

Assertion

Ref	Expression
df-dom	|- ~<_ = { <. x , y >. | E. f f : x -1-1-> y }

Distinct variable group:   x, y, f

Detailed syntax breakdown of Definition df-dom

Step	Hyp	Ref	Expression
1		cdom 7566	. 2 class ~<_
2		vx	. . . . . 6 setvar x
3	2	cv 1436	. . . . 5 class x
4		vy	. . . . . 6 setvar y
5	4	cv 1436	. . . . 5 class y
6		vf	. . . . . 6 setvar f
7	6	cv 1436	. . . . 5 class f
8	3, 5, 7	wf1 5589	. . . 4 wff f : x -1-1-> y
9	8, 6	wex 1659	. . 3 wff E. f f : x -1-1-> y
10	9, 2, 4	copab 4474	. 2 class { <. x , y >. | E. f f : x -1-1-> y }
11	1, 10	wceq 1437	1 wff ~<_ = { <. x , y >. | E. f f : x -1-1-> y }

This definition is referenced by:  reldom  7574  brdomg  7578  enssdom  7592