Theorem dfnn2 8722

Description: Definition of the set of positive integers. Another name for df-inn 8721. (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 8721	1 |- NN = |^| { x | ( 1 e. x /\ A. y e. x ( y + 1 ) e. x ) }

Syntax hints:   /\ wa 103   = wceq 1331   e. wcel 1480   {cab 2125   A.wral 2416   |^|cint 3771  (class class class)co 5774   1c1 7621   + caddc 7623   NNcn 8720

This theorem depends on definitions:  df-inn 8721

This theorem is referenced by:  peano5nni  8723  1nn  8731  peano2nn  8732  arch  8974  caucvgre  10753