Theorem ren0 44597

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 11213	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4329	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2932  ∅c0 4314  ℝcr 11105  0cc0 11106

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-1cn 11164  ax-addrcl 11167  ax-rnegex 11177  ax-cnre 11179

This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-ne 2933  df-rex 3063  df-dif 3943  df-nul 4315

This theorem is referenced by:  limsup0  44895  limsuppnfdlem  44902  limsup10ex  44974  liminf10ex  44975