Theorem rpsscn 43120

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 11174	. 2 ⊢ ℝ ⊆ ℂ
3	1, 2	sstri 3947	1 ⊢ ℝ+ ⊆ ℂ

This proof depends on syntax axioms:   ⊆ wss 3906  ℂcc 11115  ℝcr 11116  ℝ⁺crp 13034

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737  ax-resscn 11174

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-rab 3419  df-ss 3923  df-rp 13035

This theorem is used by:  readvrec2  43182