Theorem dfnn2 8921

Description: Definition of the set of positive integers. Another name for df-inn 8920. (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 8920	1 |- NN = |^| { x | ( 1 e. x /\ A. y e. x ( y + 1 ) e. x ) }

Syntax hints:   /\ wa 104   = wceq 1353   e. wcel 2148   {cab 2163   A.wral 2455   |^|cint 3845  (class class class)co 5875   1c1 7812   + caddc 7814   NNcn 8919

This theorem depends on definitions:  df-inn 8920

This theorem is referenced by:  peano5nni  8922  1nn  8930  peano2nn  8931  arch  9173  caucvgre  10990