Users' Mathboxes Mathbox for Glauco Siliprandi < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  rrpsscn Structured version   Visualization version   GIF version

Theorem rrpsscn 40240
Description: The positive reals are a subset of the complex numbers. (Contributed by Glauco Siliprandi, 29-Jun-2017.)
Assertion
Ref Expression
rrpsscn + ⊆ ℂ

Proof of Theorem rrpsscn
StepHypRef Expression
1 rpcn 11955 . 2 (𝑥 ∈ ℝ+𝑥 ∈ ℂ)
21ssriv 3713 1 + ⊆ ℂ
Colors of variables: wff setvar class
Syntax hints:  wss 3680  cc 10047  +crp 11946
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-10 2132  ax-11 2147  ax-12 2160  ax-13 2355  ax-ext 2704  ax-resscn 10106
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1599  df-ex 1818  df-nf 1823  df-sb 2011  df-clab 2711  df-cleq 2717  df-clel 2720  df-nfc 2855  df-rab 3023  df-in 3687  df-ss 3694  df-rp 11947
This theorem is referenced by:  stirlinglem8  40718
  Copyright terms: Public domain W3C validator