Theorem dfnn2 8041

Description: Definition of the set of positive integers. Another name for df-inn 8040. (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 8040	1 |- NN = |^| { x | ( 1 e. x /\ A. y e. x ( y + 1 ) e. x ) }

Syntax hints:   /\ wa 102   = wceq 1284   e. wcel 1433   {cab 2067   A.wral 2348   |^|cint 3636  (class class class)co 5532   1c1 6982   + caddc 6984   NNcn 8039

This theorem depends on definitions:  df-inn 8040

This theorem is referenced by:  peano5nni  8042  1nn  8050  peano2nn  8051  arch  8285  caucvgre  9867