Theorem zrei 12564

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 12562	. 2 ⊢ (𝐴 ∈ ℤ → 𝐴 ∈ ℝ)
3	1, 2	ax-mp 5	1 ⊢ 𝐴 ∈ ℝ

Syntax hints:   ∈ wcel 2107  ℝcr 11109  ℤcz 12558

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 2704

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 2711  df-cleq 2725  df-clel 2811  df-rab 3434  df-v 3477  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4324  df-if 4530  df-sn 4630  df-pr 4632  df-op 4636  df-uni 4910  df-br 5150  df-iota 6496  df-fv 6552  df-ov 7412  df-neg 11447  df-z 12559

This theorem is referenced by:  dfuzi  12653  eluzaddiOLD  12854  eluzsubiOLD  12856  dvdslelem  16252  divalglem1  16337  divalglem6  16341  divalglem9  16344  gcdaddmlem  16465  basellem9  26593  axlowdimlem16  28215  poimirlem17  36505  poimirlem19  36507  poimirlem20  36508  fdc  36613  jm2.27dlem2  41749