Definition df-dom 4369

Description: Define the dominance relation. For an alternate definition see dfdom2 4384. Compare Definition of [Enderton] p. 145. Typical textbook definitions are derived as brdom 4378 and domen 4379.

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 4365	. 2 class ~<_
2		vx	. . . . . 6 set x
3	2	cv 955	. . . . 5 class x
4		vy	. . . . . 6 set y
5	4	cv 955	. . . . 5 class y
6		vf	. . . . . 6 set f
7	6	cv 955	. . . . 5 class f
8	3, 5, 7	wf1 3179	. . . 4 wff f:x-1-1->y
9	8, 6	wex 980	. . 3 wff E.f f:x-1-1->y
10	9, 2, 4	copab 2666	. 2 class {<.x, y>. | E.f f:x-1-1->y}
11	1, 10	wceq 956	1 wff ~<_ = {<.x, y>. | E.f f:x-1-1->y}

This definition is referenced by:  reldom 4373  brdomg 4376  enssdom 4383

Copyright terms: Public domain