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Definition df-en 8967
Description: Define the equinumerosity relation. Definition of [Enderton] p. 129. We define to be a binary relation rather than a connective, so its arguments must be sets to be meaningful. This is acceptable because we do not consider equinumerosity for proper classes. We derive the usual definition as bren 8976. (Contributed by NM, 28-Mar-1998.)
Assertion
Ref Expression
df-en ≈ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
Distinct variable group:   𝑥,𝑦,𝑓

Detailed syntax breakdown of Definition df-en
StepHypRef Expression
1 cen 8963 . 2 class
2 vx . . . . . 6 setvar 𝑥
32cv 1533 . . . . 5 class 𝑥
4 vy . . . . . 6 setvar 𝑦
54cv 1533 . . . . 5 class 𝑦
6 vf . . . . . 6 setvar 𝑓
76cv 1533 . . . . 5 class 𝑓
83, 5, 7wf1o 6545 . . . 4 wff 𝑓:𝑥1-1-onto𝑦
98, 6wex 1774 . . 3 wff 𝑓 𝑓:𝑥1-1-onto𝑦
109, 2, 4copab 5207 . 2 class {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
111, 10wceq 1534 1 wff ≈ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  relen  8971  breng  8975  brenOLD  8977  enssdom  9000
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