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Theorem ren0 43432
Description: The set of reals is nonempty. (Contributed by Glauco Siliprandi, 23-Oct-2021.)
Assertion
Ref Expression
ren0 ℝ ≠ ∅

Proof of Theorem ren0
StepHypRef Expression
1 0re 11091 . 2 0 ∈ ℝ
21ne0ii 4296 1 ℝ ≠ ∅
Colors of variables: wff setvar class
Syntax hints:  wne 2942  c0 4281  cr 10984  0cc0 10985
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2709  ax-1cn 11043  ax-addrcl 11046  ax-rnegex 11056  ax-cnre 11058
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2816  df-ne 2943  df-rex 3073  df-dif 3912  df-nul 4282
This theorem is referenced by:  limsup0  43726  limsuppnfdlem  43733  limsup10ex  43805  liminf10ex  43806
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