Theorem rrpsscn 46040

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 12951	. 2 ⊢ (𝑥 ∈ ℝ+ → 𝑥 ∈ ℂ)
2	1	ssriv 3926	1 ⊢ ℝ+ ⊆ ℂ

Syntax hints:   ⊆ wss 3890  ℂcc 11034  ℝ⁺crp 12940

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712  ax-resscn 11093

This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-rab 3393  df-ss 3907  df-rp 12941

This theorem is referenced by:  stirlinglem8  46531