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Definition df-dom 8125
Description: Define the dominance relation. For an alternate definition see dfdom2 8149. Compare Definition of [Enderton] p. 145. Typical textbook definitions are derived as brdom 8135 and domen 8136. (Contributed by NM, 28-Mar-1998.)
Assertion
Ref Expression
df-dom ≼ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1𝑦}
Distinct variable group:   𝑥,𝑦,𝑓

Detailed syntax breakdown of Definition df-dom
StepHypRef Expression
1 cdom 8121 . 2 class
2 vx . . . . . 6 setvar 𝑥
32cv 1631 . . . . 5 class 𝑥
4 vy . . . . . 6 setvar 𝑦
54cv 1631 . . . . 5 class 𝑦
6 vf . . . . . 6 setvar 𝑓
76cv 1631 . . . . 5 class 𝑓
83, 5, 7wf1 6046 . . . 4 wff 𝑓:𝑥1-1𝑦
98, 6wex 1853 . . 3 wff 𝑓 𝑓:𝑥1-1𝑦
109, 2, 4copab 4864 . 2 class {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1𝑦}
111, 10wceq 1632 1 wff ≼ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  reldom  8129  brdomg  8133  enssdom  8148
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