Theorem zrei 9485

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 9483	. 2 |- ( A e. ZZ -> A e. RR )
3	1, 2	ax-mp 5	1 |- A e. RR

Syntax hints:   e. wcel 2202   RRcr 8031   ZZcz 9479

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-3or 1005  df-3an 1006  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-rex 2516  df-rab 2519  df-v 2804  df-un 3204  df-sn 3675  df-pr 3676  df-op 3678  df-uni 3894  df-br 4089  df-iota 5286  df-fv 5334  df-ov 6021  df-neg 8353  df-z 9480

This theorem is referenced by:  dfuzi  9590  eluzaddi  9783  eluzsubi  9784  fldiv4lem1div2  10567