Theorem rpsscn 42311

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 13039	. 2 ⊢ ℝ+ ⊆ ℝ
2		ax-resscn 11209	. 2 ⊢ ℝ ⊆ ℂ
3	1, 2	sstri 4004	1 ⊢ ℝ+ ⊆ ℂ

Syntax hints:   ⊆ wss 3962  ℂcc 11150  ℝcr 11151  ℝ⁺crp 13031

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705  ax-resscn 11209

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-rab 3433  df-ss 3979  df-rp 13032

This theorem is referenced by:  readvrec2  42369