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Theorem zrei 12512
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 12510 . 2 (𝐴 ∈ ℤ → 𝐴 ∈ ℝ)
31, 2ax-mp 5 1 𝐴 ∈ ℝ
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  cr 11057  cz 12506
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3or 1089  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-rab 3411  df-v 3450  df-dif 3918  df-un 3920  df-in 3922  df-ss 3932  df-nul 4288  df-if 4492  df-sn 4592  df-pr 4594  df-op 4598  df-uni 4871  df-br 5111  df-iota 6453  df-fv 6509  df-ov 7365  df-neg 11395  df-z 12507
This theorem is referenced by:  dfuzi  12601  eluzaddiOLD  12802  eluzsubiOLD  12804  dvdslelem  16198  divalglem1  16283  divalglem6  16287  divalglem9  16290  gcdaddmlem  16411  basellem9  26454  axlowdimlem16  27948  poimirlem17  36124  poimirlem19  36126  poimirlem20  36127  fdc  36233  jm2.27dlem2  41363
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