Theorem rpssxr 45483

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 12966	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11225	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3959	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3917  ℝcr 11074  ℝ^*cxr 11214  ℝ⁺crp 12958

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-rab 3409  df-v 3452  df-un 3922  df-ss 3934  df-xr 11219  df-rp 12959

This theorem is referenced by:  cnrefiisplem  45834