Theorem ren0 44707

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 11238	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4333	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2935  ∅c0 4318  ℝcr 11129  0cc0 11130

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2698  ax-1cn 11188  ax-addrcl 11191  ax-rnegex 11201  ax-cnre 11203

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2705  df-cleq 2719  df-clel 2805  df-ne 2936  df-rex 3066  df-dif 3947  df-nul 4319

This theorem is referenced by:  limsup0  45005  limsuppnfdlem  45012  limsup10ex  45084  liminf10ex  45085