Theorem ren0 40369

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 10330	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4124	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2971  ∅c0 4115  ℝcr 10223  0cc0 10224

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-ext 2777  ax-1cn 10282  ax-addrcl 10285  ax-rnegex 10295  ax-cnre 10297

This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2786  df-cleq 2792  df-clel 2795  df-nfc 2930  df-ne 2972  df-ral 3094  df-rex 3095  df-v 3387  df-dif 3772  df-nul 4116

This theorem is referenced by:  limsup0  40670  limsuppnfdlem  40677  limsup10ex  40749  liminf10ex  40750