Theorem rpssxr 45430

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 13039	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11302	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 4004	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3962  ℝcr 11151  ℝ^*cxr 11291  ℝ⁺crp 13031

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1539  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-rab 3433  df-v 3479  df-un 3967  df-ss 3979  df-xr 11296  df-rp 13032

This theorem is referenced by:  cnrefiisplem  45784