Theorem ren0 44112

Description: The set of reals is nonempty. (Contributed by Glauco Siliprandi, 23-Oct-2021.)

Assertion

Ref	Expression
ren0	⊢ ℝ ≠ ∅

Proof of Theorem ren0

Step	Hyp	Ref	Expression
1		0re 11216	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4338	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2941  ∅c0 4323  ℝcr 11109  0cc0 11110

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 2704  ax-1cn 11168  ax-addrcl 11171  ax-rnegex 11181  ax-cnre 11183

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 2711  df-cleq 2725  df-clel 2811  df-ne 2942  df-rex 3072  df-dif 3952  df-nul 4324

This theorem is referenced by:  limsup0  44410  limsuppnfdlem  44417  limsup10ex  44489  liminf10ex  44490