Theorem ren0 45352

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 11261	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4350	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2938  ∅c0 4339  ℝcr 11152  0cc0 11153

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-1cn 11211  ax-addrcl 11214  ax-rnegex 11224  ax-cnre 11226

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-ne 2939  df-rex 3069  df-dif 3966  df-nul 4340

This theorem is referenced by:  limsup0  45650  limsuppnfdlem  45657  limsup10ex  45729  liminf10ex  45730