Theorem rpssxr 46490

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 13128	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 11353	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3917	1 ⊢ ℝ+ ⊆ ℝ*

This proof depends on syntax axioms:   ⊆ wss 3895  ℝcr 11199  ℝ^*cxr 11342  ℝ⁺crp 13120

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-rab 3413  df-v 3452  df-ss 3896  df-un 4151  df-xr 11347  df-rp 13121

This theorem is used by:  cnrefiisplem  46839