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Theorem rpssxr 42059
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 12384 . 2 + ⊆ ℝ
2 ressxr 10674 . 2 ℝ ⊆ ℝ*
31, 2sstri 3951 1 + ⊆ ℝ*
Colors of variables: wff setvar class
Syntax hints:  wss 3908  cr 10525  *cxr 10663  +crp 12377
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 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2178  ax-ext 2794
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-nfc 2962  df-rab 3139  df-v 3471  df-un 3913  df-in 3915  df-ss 3925  df-xr 10668  df-rp 12378
This theorem is referenced by:  cnrefiisplem  42410
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