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Theorem nnrei 8991
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 8989 . 2 (𝐴 ∈ ℕ → 𝐴 ∈ ℝ)
31, 2ax-mp 5 1 𝐴 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 2164  cr 7871  cn 8982
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 2175  ax-sep 4147  ax-cnex 7963  ax-resscn 7964  ax-1re 7966  ax-addrcl 7969
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-ral 2477  df-v 2762  df-in 3159  df-ss 3166  df-int 3871  df-inn 8983
This theorem is referenced by:  nncni  8992  nnap0i  9013  nnne0i  9014  10re  9466  numlt  9472  numltc  9473  ef01bndlem  11899  pockthi  12496  strleun  12722  strle1g  12724  2strbasg  12737  2stropg  12738  tsetndxnbasendx  12808  plendxnbasendx  12822  dsndxnbasendx  12833  unifndxnbasendx  12843  slotsdifunifndx  12845
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