Theorem rpssxr 45166

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 13045	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11315	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 4001	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3959  ℝcr 11164  ℝ^*cxr 11304  ℝ⁺crp 13038

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2102  ax-9 2110  ax-ext 2700

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1537  df-ex 1775  df-sb 2062  df-clab 2707  df-cleq 2721  df-clel 2806  df-rab 3429  df-v 3474  df-un 3964  df-ss 3976  df-xr 11309  df-rp 13039

This theorem is referenced by:  cnrefiisplem  45520