Theorem rpssxr 43055

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 12765	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11047	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3932	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3889  ℝcr 10898  ℝ^*cxr 11036  ℝ⁺crp 12758

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2103  ax-9 2111  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1540  df-ex 1778  df-sb 2063  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3224  df-v 3436  df-un 3894  df-in 3896  df-ss 3906  df-xr 11041  df-rp 12759

This theorem is referenced by:  cnrefiisplem  43405