Theorem rrpsscn 41889

Description: The positive reals are a subset of the complex numbers. (Contributed by Glauco Siliprandi, 29-Jun-2017.)

Assertion

Ref	Expression
rrpsscn	⊢ ℝ+ ⊆ ℂ

Proof of Theorem rrpsscn

Step	Hyp	Ref	Expression
1		rpcn 12400	. 2 ⊢ (𝑥 ∈ ℝ+ → 𝑥 ∈ ℂ)
2	1	ssriv 3971	1 ⊢ ℝ+ ⊆ ℂ

Syntax hints:   ⊆ wss 3936  ℂcc 10535  ℝ⁺crp 12390

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2793  ax-resscn 10594

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-rab 3147  df-in 3943  df-ss 3952  df-rp 12391

This theorem is referenced by:  stirlinglem8  42386