Theorem ren0 45760

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 11146	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4298	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2933  ∅c0 4287  ℝcr 11037  0cc0 11038

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-1cn 11096  ax-addrcl 11099  ax-rnegex 11109  ax-cnre 11111

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-ne 2934  df-rex 3063  df-dif 3906  df-nul 4288

This theorem is referenced by:  limsup0  46052  limsuppnfdlem  46059  limsup10ex  46131  liminf10ex  46132