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Theorem zssxr 39434
 Description: The integers are a subset of the extended reals. (Contributed by Glauco Siliprandi, 23-Oct-2021.)
Assertion
Ref Expression
zssxr ℤ ⊆ ℝ*

Proof of Theorem zssxr
StepHypRef Expression
1 zssre 11369 . 2 ℤ ⊆ ℝ
2 ressxr 10068 . 2 ℝ ⊆ ℝ*
31, 2sstri 3604 1 ℤ ⊆ ℝ*
 Colors of variables: wff setvar class Syntax hints:   ⊆ wss 3567  ℝcr 9920  ℝ*cxr 10058  ℤcz 11362 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3or 1037  df-3an 1038  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-rex 2915  df-rab 2918  df-v 3197  df-dif 3570  df-un 3572  df-in 3574  df-ss 3581  df-nul 3908  df-if 4078  df-sn 4169  df-pr 4171  df-op 4175  df-uni 4428  df-br 4645  df-iota 5839  df-fv 5884  df-ov 6638  df-xr 10063  df-neg 10254  df-z 11363 This theorem is referenced by:  limsupequzlem  39754
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