Theorem zrei 12325

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 12323	. 2 ⊢ (𝐴 ∈ ℤ → 𝐴 ∈ ℝ)
3	1, 2	ax-mp 5	1 ⊢ 𝐴 ∈ ℝ

Syntax hints:   ∈ wcel 2106  ℝcr 10870  ℤcz 12319

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3or 1087  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-rab 3073  df-v 3434  df-dif 3890  df-un 3892  df-in 3894  df-ss 3904  df-nul 4257  df-if 4460  df-sn 4562  df-pr 4564  df-op 4568  df-uni 4840  df-br 5075  df-iota 6391  df-fv 6441  df-ov 7278  df-neg 11208  df-z 12320

This theorem is referenced by:  dfuzi  12411  eluzaddi  12611  eluzsubi  12612  dvdslelem  16018  divalglem1  16103  divalglem6  16107  divalglem9  16110  gcdaddmlem  16231  basellem9  26238  axlowdimlem16  27325  poimirlem17  35794  poimirlem19  35796  poimirlem20  35797  fdc  35903  jm2.27dlem2  40832