Theorem dfnn2 8992

Description: Definition of the set of positive integers. Another name for df-inn 8991. (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 8991	1 |- NN = |^| { x | ( 1 e. x /\ A. y e. x ( y + 1 ) e. x ) }

Syntax hints:   /\ wa 104   = wceq 1364   e. wcel 2167   {cab 2182   A.wral 2475   |^|cint 3874  (class class class)co 5922   1c1 7880   + caddc 7882   NNcn 8990

This theorem depends on definitions:  df-inn 8991

This theorem is referenced by:  peano5nni  8993  1nn  9001  peano2nn  9002  arch  9246  caucvgre  11146