Theorem zrei 9197

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 9195	. 2 |- ( A e. ZZ -> A e. RR )
3	1, 2	ax-mp 5	1 |- A e. RR

Syntax hints:   e. wcel 2136   RRcr 7752   ZZcz 9191

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-3or 969  df-3an 970  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-rex 2450  df-rab 2453  df-v 2728  df-un 3120  df-sn 3582  df-pr 3583  df-op 3585  df-uni 3790  df-br 3983  df-iota 5153  df-fv 5196  df-ov 5845  df-neg 8072  df-z 9192

This theorem is referenced by:  dfuzi  9301  eluzaddi  9492  eluzsubi  9493