Theorem ren0 45413

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 11263	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4344	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2940  ∅c0 4333  ℝcr 11154  0cc0 11155

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-1cn 11213  ax-addrcl 11216  ax-rnegex 11226  ax-cnre 11228

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ne 2941  df-rex 3071  df-dif 3954  df-nul 4334

This theorem is referenced by:  limsup0  45709  limsuppnfdlem  45716  limsup10ex  45788  liminf10ex  45789