Theorem rpsscn 42315

Description: The positive reals are a subset of the complex numbers. (Contributed by SN, 1-Oct-2025.)

Assertion

Ref	Expression
rpsscn	⊢ ℝ+ ⊆ ℂ

Proof of Theorem rpsscn

Step	Hyp	Ref	Expression
1		rpssre 13021	. 2 ⊢ ℝ+ ⊆ ℝ
2		ax-resscn 11191	. 2 ⊢ ℝ ⊆ ℂ
3	1, 2	sstri 3973	1 ⊢ ℝ+ ⊆ ℂ

Syntax hints:   ⊆ wss 3931  ℂcc 11132  ℝcr 11133  ℝ⁺crp 13013

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2708  ax-resscn 11191

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-sb 2066  df-clab 2715  df-cleq 2728  df-clel 2810  df-rab 3421  df-ss 3948  df-rp 13014

This theorem is referenced by:  readvrec2  42371