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

Theorem rpssxr 43723
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 12923 . 2 + ⊆ ℝ
2 ressxr 11200 . 2 ℝ ⊆ ℝ*
31, 2sstri 3954 1 + ⊆ ℝ*
Colors of variables: wff setvar class
Syntax hints:  wss 3911  cr 11051  *cxr 11189  +crp 12916
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-rab 3409  df-v 3448  df-un 3916  df-in 3918  df-ss 3928  df-xr 11194  df-rp 12917
This theorem is referenced by:  cnrefiisplem  44077
  Copyright terms: Public domain W3C validator