Theorem rpsscn 42673

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 12925	. 2 ⊢ ℝ+ ⊆ ℝ
2		ax-resscn 11095	. 2 ⊢ ℝ ⊆ ℂ
3	1, 2	sstri 3945	1 ⊢ ℝ+ ⊆ ℂ

Syntax hints:   ⊆ wss 3903  ℂcc 11036  ℝcr 11037  ℝ⁺crp 12917

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-resscn 11095

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rab 3402  df-ss 3920  df-rp 12918

This theorem is referenced by:  readvrec2  42735