Theorem ren0 45562

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 11125	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4293	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2929  ∅c0 4282  ℝcr 11016  0cc0 11017

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2705  ax-1cn 11075  ax-addrcl 11078  ax-rnegex 11088  ax-cnre 11090

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2712  df-cleq 2725  df-clel 2808  df-ne 2930  df-rex 3058  df-dif 3901  df-nul 4283

This theorem is referenced by:  limsup0  45854  limsuppnfdlem  45861  limsup10ex  45933  liminf10ex  45934