Theorem rpsscn 42776

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 12941	. 2 ⊢ ℝ+ ⊆ ℝ
2		ax-resscn 11086	. 2 ⊢ ℝ ⊆ ℂ
3	1, 2	sstri 3924	1 ⊢ ℝ+ ⊆ ℂ

Syntax hints:   ⊆ wss 3883  ℂcc 11027  ℝcr 11028  ℝ⁺crp 12933

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711  ax-resscn 11086

This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-rab 3392  df-ss 3900  df-rp 12934

This theorem is referenced by:  readvrec2  42838