Mathbox for Glauco Siliprandi < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ssrexr Structured version   Visualization version   GIF version

Theorem ssrexr 41999
 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 10683 . 2 ℝ ⊆ ℝ*
31, 2sstrdi 3965 1 (𝜑𝐴 ⊆ ℝ*)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ⊆ wss 3919  ℝcr 10534  ℝ*cxr 10672 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 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2796 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-v 3482  df-un 3924  df-in 3926  df-ss 3936  df-xr 10677 This theorem is referenced by:  limsuppnfdlem  42273  liminfval2  42340
 Copyright terms: Public domain W3C validator