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Theorem zssre 8913
Description: The integers are a subset of the reals. (Contributed by NM, 2-Aug-2004.)
Assertion
Ref Expression
zssre ℤ ⊆ ℝ

Proof of Theorem zssre
StepHypRef Expression
1 zre 8910 . 2 (𝑥 ∈ ℤ → 𝑥 ∈ ℝ)
21ssriv 3051 1 ℤ ⊆ ℝ
Colors of variables: wff set class
Syntax hints:  wss 3021  cr 7499  cz 8906
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 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082
This theorem depends on definitions:  df-bi 116  df-3or 931  df-3an 932  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-rex 2381  df-rab 2384  df-v 2643  df-un 3025  df-in 3027  df-ss 3034  df-sn 3480  df-pr 3481  df-op 3483  df-uni 3684  df-br 3876  df-iota 5024  df-fv 5067  df-ov 5709  df-neg 7807  df-z 8907
This theorem is referenced by:  suprzclex  9001  zred  9025  lbzbi  9258  fzval2  9634  seq3coll  10426  summodclem2a  10989  fsum3cvg3  11004  zsupcl  11435  infssuzex  11437  infssuzcldc  11439  gcddvds  11447  dvdslegcd  11448
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