Theorem rpssxr 45396

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 13064	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11334	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 4018	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3976  ℝcr 11183  ℝ^*cxr 11323  ℝ⁺crp 13057

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 2110  ax-9 2118  ax-ext 2711

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-tru 1540  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-rab 3444  df-v 3490  df-un 3981  df-ss 3993  df-xr 11328  df-rp 13058

This theorem is referenced by:  cnrefiisplem  45750