Theorem rpssxr 44181

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 12980	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11257	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3991	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3948  ℝcr 11108  ℝ^*cxr 11246  ℝ⁺crp 12973

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-rab 3433  df-v 3476  df-un 3953  df-in 3955  df-ss 3965  df-xr 11251  df-rp 12974

This theorem is referenced by:  cnrefiisplem  44535