Theorem rpssxr 45491

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 13042	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11305	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3993	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3951  ℝcr 11154  ℝ^*cxr 11294  ℝ⁺crp 13034

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 2007  ax-8 2110  ax-9 2118  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3437  df-v 3482  df-un 3956  df-ss 3968  df-xr 11299  df-rp 13035

This theorem is referenced by:  cnrefiisplem  45844