Theorem ren0 46685

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 11349	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4293	1 ⊢ ℝ ≠ ∅

This proof depends on syntax axioms:   ≠ wne 2959  ∅c0 4281  ℝcr 11238  0cc0 11239

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735  ax-1cn 11297  ax-addrcl 11300  ax-rnegex 11310  ax-cnre 11312

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-ne 2960  df-rex 3091  df-dif 4050  df-nul 4282

This theorem is used by:  limsup0  46977  limsuppnfdlem  46984  limsup10ex  47056  liminf10ex  47057