Theorem rpsscn 43080

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 13019	. 2 ⊢ ℝ+ ⊆ ℝ
2		ax-resscn 11152	. 2 ⊢ ℝ ⊆ ℂ
3	1, 2	sstri 3946	1 ⊢ ℝ+ ⊆ ℂ

Syntax hints:   ⊆ wss 3905  ℂcc 11093  ℝcr 11094  ℝ⁺crp 13011

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735  ax-resscn 11152

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-rab 3417  df-ss 3922  df-rp 13012

This theorem is referenced by:  readvrec2  43142