Theorem rpsscn 42908

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 13001	. 2 ⊢ ℝ+ ⊆ ℝ
2		ax-resscn 11130	. 2 ⊢ ℝ ⊆ ℂ
3	1, 2	sstri 3945	1 ⊢ ℝ+ ⊆ ℂ

Syntax hints:   ⊆ wss 3904  ℂcc 11071  ℝcr 11072  ℝ⁺crp 12993

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-8 2144  ax-9 2152  ax-ext 2734  ax-resscn 11130

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1800  df-sb 2091  df-clab 2741  df-cleq 2754  df-clel 2837  df-rab 3415  df-ss 3921  df-rp 12994

This theorem is referenced by:  readvrec2  42970