Theorem ren0 41668

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 10637	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4302	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 3016  ∅c0 4290  ℝcr 10530  0cc0 10531

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-8 2112  ax-9 2120  ax-ext 2793  ax-1cn 10589  ax-addrcl 10592  ax-rnegex 10602  ax-cnre 10604

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1777  df-sb 2066  df-clab 2800  df-cleq 2814  df-clel 2893  df-ne 3017  df-ral 3143  df-rex 3144  df-dif 3938  df-nul 4291

This theorem is referenced by:  limsup0  41968  limsuppnfdlem  41975  limsup10ex  42047  liminf10ex  42048