Theorem rpssxr 42120

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 12384	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 10674	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3924	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3881  ℝcr 10525  ℝ^*cxr 10663  ℝ⁺crp 12377

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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-rab 3115  df-v 3443  df-un 3886  df-in 3888  df-ss 3898  df-xr 10668  df-rp 12378

This theorem is referenced by:  cnrefiisplem  42471