Theorem rpssxr 39711

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 11843	. 2 ⊢ ℝ+ ⊆ ℝ
2		ressxr 10083	. 2 ⊢ ℝ ⊆ ℝ*
3	1, 2	sstri 3612	1 ⊢ ℝ+ ⊆ ℝ*

Syntax hints:   ⊆ wss 3574  ℝcr 9935  ℝ^*cxr 10073  ℝ⁺crp 11832

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-rab 2921  df-v 3202  df-un 3579  df-in 3581  df-ss 3588  df-xr 10078  df-rp 11833

This theorem is referenced by:  cnrefiisplem  40055