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Theorem dfnn2 8741
Description: Definition of the set of positive integers. Another name for df-inn 8740. (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 8740 1 ℕ = {𝑥 ∣ (1 ∈ 𝑥 ∧ ∀𝑦𝑥 (𝑦 + 1) ∈ 𝑥)}
Colors of variables: wff set class
Syntax hints:  wa 103   = wceq 1331  wcel 1480  {cab 2125  wral 2416   cint 3774  (class class class)co 5777  1c1 7640   + caddc 7642  cn 8739
This theorem depends on definitions:  df-inn 8740
This theorem is referenced by:  peano5nni  8742  1nn  8750  peano2nn  8751  arch  8993  caucvgre  10777
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