Theorem zrei 12492

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

Step	Hyp	Ref	Expression
1		zrei.1	. 2 ⊢ 𝐴 ∈ ℤ
2		zre 12490	. 2 ⊢ (𝐴 ∈ ℤ → 𝐴 ∈ ℝ)
3	1, 2	ax-mp 5	1 ⊢ 𝐴 ∈ ℝ

Syntax hints:   ∈ wcel 2113  ℝcr 11023  ℤcz 12486

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  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 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2713  df-cleq 2726  df-clel 2809  df-rab 3398  df-v 3440  df-dif 3902  df-un 3904  df-ss 3916  df-nul 4284  df-if 4478  df-sn 4579  df-pr 4581  df-op 4585  df-uni 4862  df-br 5097  df-iota 6446  df-fv 6498  df-ov 7359  df-neg 11365  df-z 12487

This theorem is referenced by:  dfuzi  12581  dvdslelem  16234  divalglem1  16319  divalglem6  16323  divalglem9  16326  gcdaddmlem  16449  basellem9  27053  axlowdimlem16  28979  poimirlem17  37777  poimirlem19  37779  poimirlem20  37780  fdc  37885  jm2.27dlem2  43194