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Definition df-en 8958
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 8967. (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 8954 . 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 6541 . . . 4 wff 𝑓:𝑥1-1-onto𝑦
98, 6wex 1774 . . 3 wff 𝑓 𝑓:𝑥1-1-onto𝑦
109, 2, 4copab 5204 . 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  8962  breng  8966  brenOLD  8968  enssdom  8991
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