Theorem zrei 9650

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 9648	. 2 |- ( A e. ZZ -> A e. RR )
3	1, 2	ax-mp 5	1 |- A e. RR

This proof depends on syntax axioms:   e. wcel 2209   RRcr 8178   ZZcz 9644

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-3or 1010  df-3an 1011  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-rex 2534  df-rab 2537  df-v 2823  df-un 3224  df-sn 3715  df-pr 3716  df-op 3718  df-uni 3936  df-br 4131  df-iota 5337  df-fv 5385  df-ov 6088  df-neg 8500  df-z 9645

This theorem is used by:  dfuzi  9756  eluzaddi  9949  eluzsubi  9950  fldiv4lem1div2  10742