Theorem dfnn2 9009

Description: Definition of the set of positive integers. Another name for df-inn 9008. (Contributed by Jeff Hankins, 12-Sep-2013.) (Revised by Mario Carneiro, 3-May-2014.)

Assertion

Ref	Expression
dfnn2	|- NN = |^| { x | ( 1 e. x /\ A. y e. x ( y + 1 ) e. x ) }

Distinct variable group:   x, y

Proof of Theorem dfnn2

Step	Hyp	Ref	Expression
1		df-inn 9008	1 |- NN = |^| { x | ( 1 e. x /\ A. y e. x ( y + 1 ) e. x ) }

Syntax hints:   /\ wa 104   = wceq 1364   e. wcel 2167   {cab 2182   A.wral 2475   |^|cint 3875  (class class class)co 5925   1c1 7897   + caddc 7899   NNcn 9007

This theorem depends on definitions:  df-inn 9008

This theorem is referenced by:  peano5nni  9010  1nn  9018  peano2nn  9019  arch  9263  caucvgre  11163