Theorem rpssxr 46079

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 13020	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11249	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3954	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3913  ℝcr 11095  ℝ^*cxr 11238  ℝ⁺crp 13012

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1570  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-rab 3424  df-v 3465  df-un 3918  df-ss 3930  df-xr 11243  df-rp 13013

This theorem is referenced by:  cnrefiisplem  46428