Theorem rpssxr 46227

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 13036	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11264	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3947	1 ⊢ ℝ+ ⊆ ℝ*

This proof depends on syntax axioms:   ⊆ wss 3906  ℝcr 11110  ℝ^*cxr 11253  ℝ⁺crp 13028

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-rab 3419  df-v 3459  df-un 3911  df-ss 3923  df-xr 11258  df-rp 13029

This theorem is used by:  cnrefiisplem  46576