Theorem rpssxr 45640

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 12904	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11167	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3940	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3898  ℝcr 11016  ℝ^*cxr 11156  ℝ⁺crp 12896

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2705

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2712  df-cleq 2725  df-clel 2808  df-rab 3397  df-v 3439  df-un 3903  df-ss 3915  df-xr 11161  df-rp 12897

This theorem is referenced by:  cnrefiisplem  45989