Theorem ren0 46007

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 11209	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4305	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2964  ∅c0 4294  ℝcr 11098  0cc0 11099

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741  ax-1cn 11157  ax-addrcl 11160  ax-rnegex 11170  ax-cnre 11172

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1570  df-fal 1580  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-ne 2965  df-rex 3096  df-dif 3916  df-nul 4295

This theorem is referenced by:  limsup0  46299  limsuppnfdlem  46306  limsup10ex  46378  liminf10ex  46379