Theorem ren0 45440

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 11109	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4289	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2928  ∅c0 4278  ℝcr 11000  0cc0 11001

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 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703  ax-1cn 11059  ax-addrcl 11062  ax-rnegex 11072  ax-cnre 11074

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-ne 2929  df-rex 3057  df-dif 3900  df-nul 4279

This theorem is referenced by:  limsup0  45732  limsuppnfdlem  45739  limsup10ex  45811  liminf10ex  45812