Theorem zrei 8854

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 8852	. 2 |- ( A e. ZZ -> A e. RR )
3	1, 2	ax-mp 7	1 |- A e. RR

Syntax hints:   e. wcel 1445   RRcr 7446   ZZcz 8848

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077

This theorem depends on definitions:  df-bi 116  df-3or 928  df-3an 929  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-rex 2376  df-rab 2379  df-v 2635  df-un 3017  df-sn 3472  df-pr 3473  df-op 3475  df-uni 3676  df-br 3868  df-iota 5014  df-fv 5057  df-ov 5693  df-neg 7753  df-z 8849

This theorem is referenced by:  dfuzi  8955  eluzaddi  9144  eluzsubi  9145