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Theorem nnssre 8724
 Description: The positive integers are a subset of the reals. (Contributed by NM, 10-Jan-1997.) (Revised by Mario Carneiro, 16-Jun-2013.)
Assertion
Ref Expression
nnssre

Proof of Theorem nnssre
StepHypRef Expression
1 1re 7765 . 2
2 peano2re 7898 . . 3
32rgen 2485 . 2
4 peano5nni 8723 . 2
51, 3, 4mp2an 422 1
 Colors of variables: wff set class Syntax hints:   wcel 1480  wral 2416   wss 3071  (class class class)co 5774  cr 7619  c1 7621   caddc 7623  cn 8720 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-cnex 7711  ax-resscn 7712  ax-1re 7714  ax-addrcl 7717 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-v 2688  df-in 3077  df-ss 3084  df-int 3772  df-inn 8721 This theorem is referenced by:  nnsscn  8725  nnre  8727  nnred  8733  nn0ssre  8981
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