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Theorem nnrei 8977
Description: A positive integer is a real number. (Contributed by NM, 18-Aug-1999.)
Hypothesis
Ref Expression
nnre.1  |-  A  e.  NN
Assertion
Ref Expression
nnrei  |-  A  e.  RR

Proof of Theorem nnrei
StepHypRef Expression
1 nnre.1 . 2  |-  A  e.  NN
2 nnre 8975 . 2  |-  ( A  e.  NN  ->  A  e.  RR )
31, 2ax-mp 5 1  |-  A  e.  RR
Colors of variables: wff set class
Syntax hints:    e. wcel 2160   RRcr 7857   NNcn 8968
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-sep 4143  ax-cnex 7949  ax-resscn 7950  ax-1re 7952  ax-addrcl 7955
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-v 2758  df-in 3155  df-ss 3162  df-int 3867  df-inn 8969
This theorem is referenced by:  nncni  8978  nnap0i  8999  nnne0i  9000  10re  9452  numlt  9458  numltc  9459  ef01bndlem  11873  pockthi  12470  strleun  12696  strle1g  12698  2strbasg  12711  2stropg  12712  tsetndxnbasendx  12782  plendxnbasendx  12796  dsndxnbasendx  12807  unifndxnbasendx  12817  slotsdifunifndx  12819
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