Theorem dfnn2 9306

Description: Definition of the set of positive integers. Another name for df-inn 9305. (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 9305	1 |- NN = |^| { x | ( 1 e. x /\ A. y e. x ( y + 1 ) e. x ) }

This proof depends on syntax axioms:   /\ wa 104   = wceq 1402   e. wcel 2209   {cab 2224   A.wral 2528   |^|cint 3970  (class class class)co 6085   1c1 8180   + caddc 8182   NNcn 9304

This proof depends on definitions:  df-inn 9305

This theorem is used by:  peano5nni  9307  1nn  9315  peano2nn  9316  arch  9560  caucvgre  11747