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Theorem rpssxr 45491
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 13042 . 2 + ⊆ ℝ
2 ressxr 11305 . 2 ℝ ⊆ ℝ*
31, 2sstri 3993 1 + ⊆ ℝ*
Colors of variables: wff setvar class
Syntax hints:  wss 3951  cr 11154  *cxr 11294  +crp 13034
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3437  df-v 3482  df-un 3956  df-ss 3968  df-xr 11299  df-rp 13035
This theorem is referenced by:  cnrefiisplem  45844
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