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Theorem ren0 45413
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 11263 . 2 0 ∈ ℝ
21ne0ii 4344 1 ℝ ≠ ∅
Colors of variables: wff setvar class
Syntax hints:  wne 2940  c0 4333  cr 11154  0cc0 11155
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-1cn 11213  ax-addrcl 11216  ax-rnegex 11226  ax-cnre 11228
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ne 2941  df-rex 3071  df-dif 3954  df-nul 4334
This theorem is referenced by:  limsup0  45709  limsuppnfdlem  45716  limsup10ex  45788  liminf10ex  45789
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