Theorem rrpsscn 44978

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 13022	. 2 ⊢ (𝑥 ∈ ℝ+ → 𝑥 ∈ ℂ)
2	1	ssriv 3984	1 ⊢ ℝ+ ⊆ ℂ

Syntax hints:   ⊆ wss 3947  ℂcc 11142  ℝ⁺crp 13012

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2698  ax-resscn 11201

This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2705  df-cleq 2719  df-clel 2805  df-rab 3429  df-v 3473  df-in 3954  df-ss 3964  df-rp 13013

This theorem is referenced by:  stirlinglem8  45471