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Theorem nnrei 8736
Description: A positive integer is a real number. (Contributed by NM, 18-Aug-1999.)
Hypothesis
Ref Expression
nnre.1 𝐴 ∈ ℕ
Assertion
Ref Expression
nnrei 𝐴 ∈ ℝ

Proof of Theorem nnrei
StepHypRef Expression
1 nnre.1 . 2 𝐴 ∈ ℕ
2 nnre 8734 . 2 (𝐴 ∈ ℕ → 𝐴 ∈ ℝ)
31, 2ax-mp 5 1 𝐴 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 1480  cr 7626  cn 8727
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 7718  ax-resscn 7719  ax-1re 7721  ax-addrcl 7724
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 8728
This theorem is referenced by:  nncni  8737  nnap0i  8758  nnne0i  8759  10re  9207  numlt  9213  numltc  9214  ef01bndlem  11469  strleun  12057  strle1g  12058  2strbasg  12069  2stropg  12070
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