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Theorem ren0 43285
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 11078 . 2 0 ∈ ℝ
21ne0ii 4284 1 ℝ ≠ ∅
Colors of variables: wff setvar class
Syntax hints:  wne 2940  c0 4269  cr 10971  0cc0 10972
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707  ax-1cn 11030  ax-addrcl 11033  ax-rnegex 11043  ax-cnre 11045
This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1543  df-fal 1553  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-ne 2941  df-rex 3071  df-dif 3901  df-nul 4270
This theorem is referenced by:  limsup0  43579  limsuppnfdlem  43586  limsup10ex  43658  liminf10ex  43659
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