Theorem rrpsscn 43019

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 12669	. 2 ⊢ (𝑥 ∈ ℝ+ → 𝑥 ∈ ℂ)
2	1	ssriv 3921	1 ⊢ ℝ+ ⊆ ℂ

Syntax hints:   ⊆ wss 3883  ℂcc 10800  ℝ⁺crp 12659

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709  ax-resscn 10859

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-rab 3072  df-v 3424  df-in 3890  df-ss 3900  df-rp 12660

This theorem is referenced by:  stirlinglem8  43512