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Theorem rpssxr 40227
Description: The positive reals are a subset of the extended reals. (Contributed by Glauco Siliprandi, 5-Feb-2022.)
Assertion
Ref Expression
rpssxr + ⊆ ℝ*

Proof of Theorem rpssxr
StepHypRef Expression
1 rpssre 12046 . 2 + ⊆ ℝ
2 ressxr 10285 . 2 ℝ ⊆ ℝ*
31, 2sstri 3761 1 + ⊆ ℝ*
Colors of variables: wff setvar class
Syntax hints:  wss 3723  cr 10137  *cxr 10275  +crp 12035
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 835  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-rab 3070  df-v 3353  df-un 3728  df-in 3730  df-ss 3737  df-xr 10280  df-rp 12036
This theorem is referenced by:  cnrefiisplem  40573
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