Theorem rpssxr 46693

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 13152	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11377	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3922	1 ⊢ ℝ+ ⊆ ℝ*

This proof depends on syntax axioms:   ⊆ wss 3900  ℝcr 11223  ℝ^*cxr 11366  ℝ⁺crp 13144

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rab 3417  df-v 3456  df-ss 3901  df-un 4154  df-xr 11371  df-rp 13145

This theorem is used by:  cnrefiisplem  47042