Theorem dfnn2 9040

Description: Definition of the set of positive integers. Another name for df-inn 9039. (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 9039	1 |- NN = |^| { x | ( 1 e. x /\ A. y e. x ( y + 1 ) e. x ) }

Syntax hints:   /\ wa 104   = wceq 1373   e. wcel 2176   {cab 2191   A.wral 2484   |^|cint 3885  (class class class)co 5946   1c1 7928   + caddc 7930   NNcn 9038

This theorem depends on definitions:  df-inn 9039

This theorem is referenced by:  peano5nni  9041  1nn  9049  peano2nn  9050  arch  9294  caucvgre  11325