ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  dfnn2 Structured version   GIF version

Theorem dfnn2 7697
Description: Definition of the set of positive integers. Another name for df-inn 7696. (Contributed by Jeff Hankins, 12-Sep-2013.) (Revised by Mario Carneiro, 3-May-2014.)
Assertion
Ref Expression
dfnn2 ℕ = {x ∣ (1 x y x (y + 1) x)}
Distinct variable group:   x,y

Proof of Theorem dfnn2
StepHypRef Expression
1 df-inn 7696 1 ℕ = {x ∣ (1 x y x (y + 1) x)}
Colors of variables: wff set class
Syntax hints:   wa 97   = wceq 1242   wcel 1390  {cab 2023  wral 2300   cint 3606  (class class class)co 5455  1c1 6712   + caddc 6714  cn 7695
This theorem depends on definitions:  df-inn 7696
This theorem is referenced by:  peano5nni  7698  1nn  7706  peano2nn  7707  arch  7954
  Copyright terms: Public domain W3C validator