Theorem zrei 8357

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

Step	Hyp	Ref	Expression
1		zre.1	. 2 |- A e. ZZ
2		zre 8355	. 2 |- ( A e. ZZ -> A e. RR )
3	1, 2	ax-mp 7	1 |- A e. RR

Syntax hints:   e. wcel 1433   RRcr 6980   ZZcz 8351

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 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-3or 920  df-3an 921  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-rex 2354  df-rab 2357  df-v 2603  df-un 2977  df-sn 3404  df-pr 3405  df-op 3407  df-uni 3602  df-br 3786  df-iota 4887  df-fv 4930  df-ov 5535  df-neg 7282  df-z 8352

This theorem is referenced by:  dfuzi  8457  eluzaddi  8645  eluzsubi  8646