Definition df-dom 6159

Description: Define the dominance relation. Compare Definition of [Enderton] p. 145. Typical textbook definitions are derived as brdom 6167 and domen 6168. (Contributed by NM, 28-Mar-1998.)

Assertion

Ref	Expression
df-dom	⊢ ≼ = {⟨x, y⟩ ∣ ∃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 6156	. 2 class ≼
2		vx	. . . . . 6 setvar x
3	2	cv 1241	. . . . 5 class x
4		vy	. . . . . 6 setvar y
5	4	cv 1241	. . . . 5 class y
6		vf	. . . . . 6 setvar f
7	6	cv 1241	. . . . 5 class f
8	3, 5, 7	wf1 4842	. . . 4 wff f:x–1-1→y
9	8, 6	wex 1378	. . 3 wff ∃f f:x–1-1→y
10	9, 2, 4	copab 3808	. 2 class {⟨x, y⟩ ∣ ∃f f:x–1-1→y}
11	1, 10	wceq 1242	1 wff ≼ = {⟨x, y⟩ ∣ ∃f f:x–1-1→y}

This definition is referenced by:  reldom  6162  brdomg  6165  enssdom  6178