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Theorem zred 8116
Description: An integer is a real number. (Contributed by Mario Carneiro, 28-May-2016.)
Hypothesis
Ref Expression
zred.1 (φA ℤ)
Assertion
Ref Expression
zred (φA ℝ)

Proof of Theorem zred
StepHypRef Expression
1 zssre 8008 . 2 ℤ ⊆ ℝ
2 zred.1 . 2 (φA ℤ)
31, 2sseldi 2937 1 (φA ℝ)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1390  cr 6690  cz 8001
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-bnd 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 6962  df-z 8002
This theorem is referenced by:  zcnd  8117  eluzelre  8239  eluzadd  8257  eluzsub  8258  uzm1  8259  z2ge  8489  fztri3or  8653  fznlem  8655  fzdisj  8666  fzpreddisj  8683  fznatpl1  8688  uzdisj  8705  fzm1  8712  fz0fzdiffz0  8737  elfzmlbm  8738  elfzmlbp  8740  difelfznle  8743  nn0disj  8745  elfzolt3  8763  fzonel  8766  fzouzdisj  8786  fzonmapblen  8793  fzoaddel  8798  elfzonelfzo  8836  frec2uzlt2d  8851  frec2uzf1od  8853  expival  8891
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