Theorem rpsscn 42333

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 13042	. 2 ⊢ ℝ+ ⊆ ℝ
2		ax-resscn 11212	. 2 ⊢ ℝ ⊆ ℂ
3	1, 2	sstri 3993	1 ⊢ ℝ+ ⊆ ℂ

Syntax hints:   ⊆ wss 3951  ℂcc 11153  ℝcr 11154  ℝ⁺crp 13034

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 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-resscn 11212

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3437  df-ss 3968  df-rp 13035

This theorem is referenced by:  readvrec2  42391