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Theorem dfnn2 7868
Description: Definition of the set of positive integers. Another name for df-inn 7867. (Contributed by Jeff Hankins, 12-Sep-2013.) (Revised by Mario Carneiro, 3-May-2014.)
Assertion
Ref Expression
dfnn2 ℕ = {𝑥 ∣ (1 ∈ 𝑥 ∧ ∀𝑦𝑥 (𝑦 + 1) ∈ 𝑥)}
Distinct variable group:   𝑥,𝑦

Proof of Theorem dfnn2
StepHypRef Expression
1 df-inn 7867 1 ℕ = {𝑥 ∣ (1 ∈ 𝑥 ∧ ∀𝑦𝑥 (𝑦 + 1) ∈ 𝑥)}
Colors of variables: wff set class
Syntax hints:  wa 97   = wceq 1243  wcel 1393  {cab 2026  wral 2303   cint 3612  (class class class)co 5475  1c1 6847   + caddc 6849  cn 7866
This theorem depends on definitions:  df-inn 7867
This theorem is referenced by:  peano5nni  7869  1nn  7877  peano2nn  7878  arch  8126  caucvgre  9434
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