Theorem rpssxr 45930

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 12948	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11187	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3931	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3890  ℝcr 11035  ℝ^*cxr 11176  ℝ⁺crp 12940

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-rab 3393  df-v 3434  df-un 3895  df-ss 3907  df-xr 11181  df-rp 12941

This theorem is referenced by:  cnrefiisplem  46279