Theorem rpsscn 42338

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 12898	. 2 ⊢ ℝ+ ⊆ ℝ
2		ax-resscn 11063	. 2 ⊢ ℝ ⊆ ℂ
3	1, 2	sstri 3944	1 ⊢ ℝ+ ⊆ ℂ

Syntax hints:   ⊆ wss 3902  ℂcc 11004  ℝcr 11005  ℝ⁺crp 12890

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703  ax-resscn 11063

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-rab 3396  df-ss 3919  df-rp 12891

This theorem is referenced by:  readvrec2  42400