Theorem dfnn2 8880

Description: Definition of the set of positive integers. Another name for df-inn 8879. (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 8879	1 |- NN = |^| { x | ( 1 e. x /\ A. y e. x ( y + 1 ) e. x ) }

Syntax hints:   /\ wa 103   = wceq 1348   e. wcel 2141   {cab 2156   A.wral 2448   |^|cint 3831  (class class class)co 5853   1c1 7775   + caddc 7777   NNcn 8878

This theorem depends on definitions:  df-inn 8879

This theorem is referenced by:  peano5nni  8881  1nn  8889  peano2nn  8890  arch  9132  caucvgre  10945