Theorem dfnn2 8485

Description: Definition of the set of positive integers. Another name for df-inn 8484. (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 8484	1 |- NN = |^| { x | ( 1 e. x /\ A. y e. x ( y + 1 ) e. x ) }

Syntax hints:   /\ wa 103   = wceq 1290   e. wcel 1439   {cab 2075   A.wral 2360   |^|cint 3694  (class class class)co 5666   1c1 7412   + caddc 7414   NNcn 8483

This theorem depends on definitions:  df-inn 8484

This theorem is referenced by:  peano5nni  8486  1nn  8494  peano2nn  8495  arch  8731  caucvgre  10475