Theorem rpssxr 42911

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 12666	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 10950	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3926	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3883  ℝcr 10801  ℝ^*cxr 10939  ℝ⁺crp 12659

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-rab 3072  df-v 3424  df-un 3888  df-in 3890  df-ss 3900  df-xr 10944  df-rp 12660

This theorem is referenced by:  cnrefiisplem  43260