Theorem ren0 42896

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 10961	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4276	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2944  ∅c0 4261  ℝcr 10854  0cc0 10855

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1801  ax-4 1815  ax-5 1916  ax-6 1974  ax-7 2014  ax-8 2111  ax-9 2119  ax-ext 2710  ax-1cn 10913  ax-addrcl 10916  ax-rnegex 10926  ax-cnre 10928

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1544  df-fal 1554  df-ex 1786  df-sb 2071  df-clab 2717  df-cleq 2731  df-clel 2817  df-ne 2945  df-ral 3070  df-rex 3071  df-dif 3894  df-nul 4262

This theorem is referenced by:  limsup0  43189  limsuppnfdlem  43196  limsup10ex  43268  liminf10ex  43269