Theorem rpssxr 45524

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 12898	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11156	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3944	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3902  ℝcr 11005  ℝ^*cxr 11145  ℝ⁺crp 12890

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-rab 3396  df-v 3438  df-un 3907  df-ss 3919  df-xr 11150  df-rp 12891

This theorem is referenced by:  cnrefiisplem  45873