Theorem dfnn2 9239

Description: Definition of the set of positive integers. Another name for df-inn 9238. (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 9238	1 |- NN = |^| { x | ( 1 e. x /\ A. y e. x ( y + 1 ) e. x ) }

Syntax hints:   /\ wa 104   = wceq 1398   e. wcel 2203   {cab 2218   A.wral 2520   |^|cint 3949  (class class class)co 6050   1c1 8128   + caddc 8130   NNcn 9237

This theorem depends on definitions:  df-inn 9238

This theorem is referenced by:  peano5nni  9240  1nn  9248  peano2nn  9249  arch  9493  caucvgre  11666