Definition df-dom 8810

Description: Define the dominance relation. For an alternate definition see dfdom2 8843. Compare Definition of [Enderton] p. 145. Typical textbook definitions are derived as brdom 8825 and domen 8826. (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 8806	. 2 class ≼
2		vx	. . . . . 6 setvar 𝑥
3	2	cv 1540	. . . . 5 class 𝑥
4		vy	. . . . . 6 setvar 𝑦
5	4	cv 1540	. . . . 5 class 𝑦
6		vf	. . . . . 6 setvar 𝑓
7	6	cv 1540	. . . . 5 class 𝑓
8	3, 5, 7	wf1 6480	. . . 4 wff 𝑓:𝑥–1-1→𝑦
9	8, 6	wex 1781	. . 3 wff ∃𝑓 𝑓:𝑥–1-1→𝑦
10	9, 2, 4	copab 5158	. 2 class {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥–1-1→𝑦}
11	1, 10	wceq 1541	1 wff ≼ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥–1-1→𝑦}

This definition is referenced by:  reldom  8814  brdom2g  8820  brdomgOLD  8822  enssdom  8842