Theorem rpssxr 46014

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 12994	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11219	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3943	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3902  ℝcr 11065  ℝ^*cxr 11208  ℝ⁺crp 12986

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-tru 1562  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-rab 3414  df-v 3455  df-un 3907  df-ss 3919  df-xr 11213  df-rp 12987

This theorem is referenced by:  cnrefiisplem  46363