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Theorem zrei 12617
Description: An integer is a real number. (Contributed by NM, 14-Jul-2005.)
Hypothesis
Ref Expression
zrei.1 𝐴 ∈ ℤ
Assertion
Ref Expression
zrei 𝐴 ∈ ℝ

Proof of Theorem zrei
StepHypRef Expression
1 zrei.1 . 2 𝐴 ∈ ℤ
2 zre 12615 . 2 (𝐴 ∈ ℤ → 𝐴 ∈ ℝ)
31, 2ax-mp 5 1 𝐴 ∈ ℝ
Colors of variables: wff setvar class
Syntax hints:  wcel 2106  cr 11152  cz 12611
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3or 1087  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-iota 6516  df-fv 6571  df-ov 7434  df-neg 11493  df-z 12612
This theorem is referenced by:  dfuzi  12707  eluzaddiOLD  12908  eluzsubiOLD  12910  dvdslelem  16343  divalglem1  16428  divalglem6  16432  divalglem9  16435  gcdaddmlem  16558  basellem9  27147  axlowdimlem16  28987  poimirlem17  37624  poimirlem19  37626  poimirlem20  37627  fdc  37732  jm2.27dlem2  42999
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