Theorem ren0 45317

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 11292	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4367	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2946  ∅c0 4352  ℝcr 11183  0cc0 11184

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711  ax-1cn 11242  ax-addrcl 11245  ax-rnegex 11255  ax-cnre 11257

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-ne 2947  df-rex 3077  df-dif 3979  df-nul 4353

This theorem is referenced by:  limsup0  45615  limsuppnfdlem  45622  limsup10ex  45694  liminf10ex  45695