Theorem dfnn2 8859

Description: Definition of the set of positive integers. Another name for df-inn 8858. (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 8858	1 |- NN = |^| { x | ( 1 e. x /\ A. y e. x ( y + 1 ) e. x ) }

Syntax hints:   /\ wa 103   = wceq 1343   e. wcel 2136   {cab 2151   A.wral 2444   |^|cint 3824  (class class class)co 5842   1c1 7754   + caddc 7756   NNcn 8857

This theorem depends on definitions:  df-inn 8858

This theorem is referenced by:  peano5nni  8860  1nn  8868  peano2nn  8869  arch  9111  caucvgre  10923