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Theorem ssrexr 44688
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 11257 . 2 ℝ ⊆ ℝ*
31, 2sstrdi 3987 1 (𝜑𝐴 ⊆ ℝ*)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3941  cr 11106  *cxr 11246
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468  df-un 3946  df-in 3948  df-ss 3958  df-xr 11251
This theorem is referenced by:  limsuppnfdlem  44963  liminfval2  45030
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