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Theorem zrei 8666
Description: An integer is a real number. (Contributed by NM, 14-Jul-2005.)
Hypothesis
Ref Expression
zre.1  |-  A  e.  ZZ
Assertion
Ref Expression
zrei  |-  A  e.  RR

Proof of Theorem zrei
StepHypRef Expression
1 zre.1 . 2  |-  A  e.  ZZ
2 zre 8664 . 2  |-  ( A  e.  ZZ  ->  A  e.  RR )
31, 2ax-mp 7 1  |-  A  e.  RR
Colors of variables: wff set class
Syntax hints:    e. wcel 1436   RRcr 7270   ZZcz 8660
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-3or 923  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rex 2361  df-rab 2364  df-v 2616  df-un 2990  df-sn 3431  df-pr 3432  df-op 3434  df-uni 3631  df-br 3815  df-iota 4937  df-fv 4980  df-ov 5597  df-neg 7577  df-z 8661
This theorem is referenced by:  dfuzi  8766  eluzaddi  8954  eluzsubi  8955
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