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Theorem nnrei 8887
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 8885 . 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 2141   RRcr 7773   NNcn 8878
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152  ax-sep 4107  ax-cnex 7865  ax-resscn 7866  ax-1re 7868  ax-addrcl 7871
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-ral 2453  df-v 2732  df-in 3127  df-ss 3134  df-int 3832  df-inn 8879
This theorem is referenced by:  nncni  8888  nnap0i  8909  nnne0i  8910  10re  9361  numlt  9367  numltc  9368  ef01bndlem  11719  pockthi  12310  strleun  12507  strle1g  12508  2strbasg  12519  2stropg  12520
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