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Definition df-en 7916
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 7924. (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 7912 . 2 class
2 vx . . . . . 6 setvar 𝑥
32cv 1479 . . . . 5 class 𝑥
4 vy . . . . . 6 setvar 𝑦
54cv 1479 . . . . 5 class 𝑦
6 vf . . . . . 6 setvar 𝑓
76cv 1479 . . . . 5 class 𝑓
83, 5, 7wf1o 5856 . . . 4 wff 𝑓:𝑥1-1-onto𝑦
98, 6wex 1701 . . 3 wff 𝑓 𝑓:𝑥1-1-onto𝑦
109, 2, 4copab 4682 . 2 class {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
111, 10wceq 1480 1 wff ≈ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  relen  7920  bren  7924  enssdom  7940
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