Theorem rpssxr 45908

Description: The positive reals are a subset of the extended reals. (Contributed by Glauco Siliprandi, 5-Feb-2022.)

Assertion

Ref	Expression
rpssxr	⊢ ℝ+ ⊆ ℝ*

Proof of Theorem rpssxr

Step	Hyp	Ref	Expression
1		rpssre 12950	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11189	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3931	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3889  ℝcr 11037  ℝ^*cxr 11178  ℝ⁺crp 12942

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 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-rab 3390  df-v 3431  df-un 3894  df-ss 3906  df-xr 11183  df-rp 12943

This theorem is referenced by:  cnrefiisplem  46257