Definition df-dom 7596

Description: Define the dominance relation. For an alternate definition see dfdom2 7620. Compare Definition of [Enderton] p. 145. Typical textbook definitions are derived as brdom 7606 and domen 7607. (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 7592	. 2 class ~<_
2		vx	. . . . . 6 setvar x
3	2	cv 1453	. . . . 5 class x
4		vy	. . . . . 6 setvar y
5	4	cv 1453	. . . . 5 class y
6		vf	. . . . . 6 setvar f
7	6	cv 1453	. . . . 5 class f
8	3, 5, 7	wf1 5597	. . . 4 wff f : x -1-1-> y
9	8, 6	wex 1673	. . 3 wff E. f f : x -1-1-> y
10	9, 2, 4	copab 4473	. 2 class { <. x , y >. | E. f f : x -1-1-> y }
11	1, 10	wceq 1454	1 wff ~<_ = { <. x , y >. | E. f f : x -1-1-> y }

This definition is referenced by:  reldom  7600  brdomg  7604  enssdom  7619