Theorem rpsscn 42950

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 13024	. 2 ⊢ ℝ+ ⊆ ℝ
2		ax-resscn 11157	. 2 ⊢ ℝ ⊆ ℂ
3	1, 2	sstri 3954	1 ⊢ ℝ+ ⊆ ℂ

Syntax hints:   ⊆ wss 3913  ℂcc 11098  ℝcr 11099  ℝ⁺crp 13016

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741  ax-resscn 11157

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-rab 3424  df-ss 3930  df-rp 13017

This theorem is referenced by:  readvrec2  43012