Theorem rrpsscn 46426

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 13057	. 2 ⊢ (𝑥 ∈ ℝ+ → 𝑥 ∈ ℂ)
2	1	ssriv 3938	1 ⊢ ℝ+ ⊆ ℂ

This proof depends on syntax axioms:   ⊆ wss 3902  ℂcc 11126  ℝ⁺crp 13046

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 2147  ax-9 2155  ax-ext 2734  ax-resscn 11185

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-sb 2100  df-clab 2741  df-cleq 2754  df-clel 2837  df-rab 3415  df-ss 3919  df-rp 13047

This theorem is used by:  stirlinglem8  46917