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Theorem nnrei 8697
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 8695 . 2 (𝐴 ∈ ℕ → 𝐴 ∈ ℝ)
31, 2ax-mp 5 1 𝐴 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 1465  cr 7587  cn 8688
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-sep 4016  ax-cnex 7679  ax-resscn 7680  ax-1re 7682  ax-addrcl 7685
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-ral 2398  df-v 2662  df-in 3047  df-ss 3054  df-int 3742  df-inn 8689
This theorem is referenced by:  nncni  8698  nnap0i  8719  nnne0i  8720  10re  9168  numlt  9174  numltc  9175  ef01bndlem  11390  strleun  11975  strle1g  11976  2strbasg  11987  2stropg  11988
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