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Theorem dfnn2 7992
Description: Definition of the set of positive integers. Another name for df-inn 7991. (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 7991 1 ℕ = {𝑥 ∣ (1 ∈ 𝑥 ∧ ∀𝑦𝑥 (𝑦 + 1) ∈ 𝑥)}
Colors of variables: wff set class
Syntax hints:  wa 101   = wceq 1259  wcel 1409  {cab 2042  wral 2323   cint 3643  (class class class)co 5540  1c1 6948   + caddc 6950  cn 7990
This theorem depends on definitions:  df-inn 7991
This theorem is referenced by:  peano5nni  7993  1nn  8001  peano2nn  8002  arch  8236  caucvgre  9808
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