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Theorem zssxr 43718
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 12511 . 2 ℤ ⊆ ℝ
2 ressxr 11204 . 2 ℝ ⊆ ℝ*
31, 2sstri 3954 1 ℤ ⊆ ℝ*
Colors of variables: wff setvar class
Syntax hints:  wss 3911  cr 11055  *cxr 11193  cz 12504
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3or 1089  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3407  df-v 3446  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-sn 4588  df-pr 4590  df-op 4594  df-uni 4867  df-br 5107  df-iota 6449  df-fv 6505  df-ov 7361  df-xr 11198  df-neg 11393  df-z 12505
This theorem is referenced by:  limsupequzlem  44049
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