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Theorem zred 8136
Description: An integer is a real number. (Contributed by Mario Carneiro, 28-May-2016.)
Hypothesis
Ref Expression
zred.1  ZZ
Assertion
Ref Expression
zred  RR

Proof of Theorem zred
StepHypRef Expression
1 zssre 8028 . 2  ZZ  C_  RR
2 zred.1 . 2  ZZ
31, 2sseldi 2937 1  RR
Colors of variables: wff set class
Syntax hints:   wi 4   wcel 1390   RRcr 6710   ZZcz 8021
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3or 885  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-rab 2309  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853  df-ov 5458  df-neg 6982  df-z 8022
This theorem is referenced by:  zcnd  8137  eluzelre  8259  eluzadd  8277  eluzsub  8278  uzm1  8279  z2ge  8509  fztri3or  8673  fznlem  8675  fzdisj  8686  fzpreddisj  8703  fznatpl1  8708  uzdisj  8725  fzm1  8732  fz0fzdiffz0  8757  elfzmlbm  8758  elfzmlbp  8760  difelfznle  8763  nn0disj  8765  elfzolt3  8783  fzonel  8786  fzouzdisj  8806  fzonmapblen  8813  fzoaddel  8818  elfzonelfzo  8856  frec2uzlt2d  8871  frec2uzf1od  8873  expival  8911
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