Definition df-dom 8938

Description: Define the dominance relation. For an alternate definition see dfdom2 8971. Compare Definition of [Enderton] p. 145. Typical textbook definitions are derived as brdom 8953 and domen 8954. (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 8934	. 2 class ≼
2		vx	. . . . . 6 setvar 𝑥
3	2	cv 1541	. . . . 5 class 𝑥
4		vy	. . . . . 6 setvar 𝑦
5	4	cv 1541	. . . . 5 class 𝑦
6		vf	. . . . . 6 setvar 𝑓
7	6	cv 1541	. . . . 5 class 𝑓
8	3, 5, 7	wf1 6538	. . . 4 wff 𝑓:𝑥–1-1→𝑦
9	8, 6	wex 1782	. . 3 wff ∃𝑓 𝑓:𝑥–1-1→𝑦
10	9, 2, 4	copab 5210	. 2 class {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥–1-1→𝑦}
11	1, 10	wceq 1542	1 wff ≼ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥–1-1→𝑦}

This definition is referenced by:  reldom  8942  brdom2g  8948  brdomgOLD  8950  enssdom  8970