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Theorem zrei 8251
 Description: An integer is a real number. (Contributed by NM, 14-Jul-2005.)
Hypothesis
Ref Expression
zre.1 𝐴 ∈ ℤ
Assertion
Ref Expression
zrei 𝐴 ∈ ℝ

Proof of Theorem zrei
StepHypRef Expression
1 zre.1 . 2 𝐴 ∈ ℤ
2 zre 8249 . 2 (𝐴 ∈ ℤ → 𝐴 ∈ ℝ)
31, 2ax-mp 7 1 𝐴 ∈ ℝ
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1393  ℝcr 6888  ℤcz 8245 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3or 886  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-rab 2315  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910  df-ov 5515  df-neg 7185  df-z 8246 This theorem is referenced by:  dfuzi  8348  eluzaddi  8499  eluzsubi  8500
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