Definition df-dom 5428

Description: Define the dominance relation. For an alternate definition see dfdom2 5443. Compare Definition of [Enderton] p. 145. Typical textbook definitions are derived as brdom 5437 and domen 5438.

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 5424	. 2 class ~<_
2		vx	. . . . . 6 set x
3	2	cv 1297	. . . . 5 class x
4		vy	. . . . . 6 set y
5	4	cv 1297	. . . . 5 class y
6		vf	. . . . . 6 set f
7	6	cv 1297	. . . . 5 class f
8	3, 5, 7	wf1 3995	. . . 4 wff f:x-1-1->y
9	8, 6	wex 1326	. . 3 wff E.f f:x-1-1->y
10	9, 2, 4	copab 3395	. 2 class {<.x, y>. | E.f f:x-1-1->y}
11	1, 10	wceq 1298	1 wff ~<_ = {<.x, y>. | E.f f:x-1-1->y}

This definition is referenced by:  reldom 5432  brdomg 5435  enssdom 5442

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