Theorem rpssxr 44239

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 12981	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11258	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3992	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3949  ℝcr 11109  ℝ^*cxr 11247  ℝ⁺crp 12974

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3434  df-v 3477  df-un 3954  df-in 3956  df-ss 3966  df-xr 11252  df-rp 12975

This theorem is referenced by:  cnrefiisplem  44593