Theorem rpssxr 41763

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 12399	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 10688	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3979	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3939  ℝcr 10539  ℝ^*cxr 10677  ℝ⁺crp 12392

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 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-10 2144  ax-11 2160  ax-12 2176  ax-ext 2796

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1539  df-ex 1780  df-nf 1784  df-sb 2069  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2966  df-rab 3150  df-v 3499  df-un 3944  df-in 3946  df-ss 3955  df-xr 10682  df-rp 12393

This theorem is referenced by:  cnrefiisplem  42116