Theorem rpsscn 42294

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 12966	. 2 ⊢ ℝ+ ⊆ ℝ
2		ax-resscn 11132	. 2 ⊢ ℝ ⊆ ℂ
3	1, 2	sstri 3959	1 ⊢ ℝ+ ⊆ ℂ

Syntax hints:   ⊆ wss 3917  ℂcc 11073  ℝcr 11074  ℝ⁺crp 12958

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 2702  ax-resscn 11132

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-rab 3409  df-ss 3934  df-rp 12959

This theorem is referenced by:  readvrec2  42356