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Theorem rpssxr 43621
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 12876 . 2 + ⊆ ℝ
2 ressxr 11157 . 2 ℝ ⊆ ℝ*
31, 2sstri 3951 1 + ⊆ ℝ*
Colors of variables: wff setvar class
Syntax hints:  wss 3908  cr 11008  *cxr 11146  +crp 12869
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2715  df-cleq 2729  df-clel 2815  df-rab 3406  df-v 3445  df-un 3913  df-in 3915  df-ss 3925  df-xr 11151  df-rp 12870
This theorem is referenced by:  cnrefiisplem  43971
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