Theorem dfnn2 7916

Description: Definition of the set of positive integers. Another name for df-inn 7915. (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 7915	1 |- NN = |^| { x | ( 1 e. x /\ A. y e. x ( y + 1 ) e. x ) }

Syntax hints:   /\ wa 97   = wceq 1243   e. wcel 1393   {cab 2026   A.wral 2306   |^|cint 3615  (class class class)co 5512   1c1 6890   + caddc 6892   NNcn 7914

This theorem depends on definitions:  df-inn 7915

This theorem is referenced by:  peano5nni  7917  1nn  7925  peano2nn  7926  arch  8178  caucvgre  9580