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Theorem ssrexr 44814
Description: A subset of the reals is a subset of the extended reals. (Contributed by Glauco Siliprandi, 2-Jan-2022.)
Hypothesis
Ref Expression
ssrexr.1 (𝜑𝐴 ⊆ ℝ)
Assertion
Ref Expression
ssrexr (𝜑𝐴 ⊆ ℝ*)

Proof of Theorem ssrexr
StepHypRef Expression
1 ssrexr.1 . 2 (𝜑𝐴 ⊆ ℝ)
2 ressxr 11289 . 2 ℝ ⊆ ℝ*
31, 2sstrdi 3992 1 (𝜑𝐴 ⊆ ℝ*)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3947  cr 11138  *cxr 11278
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3473  df-un 3952  df-in 3954  df-ss 3964  df-xr 11283
This theorem is referenced by:  limsuppnfdlem  45089  liminfval2  45156
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