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Theorem zrei 8308
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 8306 . 2 (𝐴 ∈ ℤ → 𝐴 ∈ ℝ)
31, 2ax-mp 7 1 𝐴 ∈ ℝ
Colors of variables: wff set class
Syntax hints:  wcel 1409  cr 6946  cz 8302
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-3or 897  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-rab 2332  df-v 2576  df-un 2950  df-sn 3409  df-pr 3410  df-op 3412  df-uni 3609  df-br 3793  df-iota 4895  df-fv 4938  df-ov 5543  df-neg 7248  df-z 8303
This theorem is referenced by:  dfuzi  8407  eluzaddi  8595  eluzsubi  8596
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