Theorem dfnn2 9123

Description: Definition of the set of positive integers. Another name for df-inn 9122. (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 9122	1 |- NN = |^| { x | ( 1 e. x /\ A. y e. x ( y + 1 ) e. x ) }

Syntax hints:   /\ wa 104   = wceq 1395   e. wcel 2200   {cab 2215   A.wral 2508   |^|cint 3923  (class class class)co 6007   1c1 8011   + caddc 8013   NNcn 9121

This theorem depends on definitions:  df-inn 9122

This theorem is referenced by:  peano5nni  9124  1nn  9132  peano2nn  9133  arch  9377  caucvgre  11508