Theorem rpsscn 43496

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 13138	. 2 ⊢ ℝ+ ⊆ ℝ
2		ax-resscn 11267	. 2 ⊢ ℝ ⊆ ℂ
3	1, 2	sstri 3921	1 ⊢ ℝ+ ⊆ ℂ

This proof depends on syntax axioms:   ⊆ wss 3899  ℂcc 11208  ℝcr 11209  ℝ⁺crp 13130

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-8 2148  ax-9 2156  ax-ext 2735  ax-resscn 11267

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812  df-sb 2101  df-clab 2742  df-cleq 2755  df-clel 2838  df-rab 3416  df-ss 3900  df-rp 13131

This theorem is used by:  readvrec2  43552