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Theorem dfnn2 8108
Description: Definition of the set of positive integers. Another name for df-inn 8107. (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
StepHypRef Expression
1 df-inn 8107 1  |-  NN  =  |^| { x  |  ( 1  e.  x  /\  A. y  e.  x  ( y  +  1 )  e.  x ) }
Colors of variables: wff set class
Syntax hints:    /\ wa 102    = wceq 1285    e. wcel 1434   {cab 2068   A.wral 2349   |^|cint 3644  (class class class)co 5543   1c1 7044    + caddc 7046   NNcn 8106
This theorem depends on definitions:  df-inn 8107
This theorem is referenced by:  peano5nni  8109  1nn  8117  peano2nn  8118  arch  8352  caucvgre  10005
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