Theorem ren0 46519

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 11315	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4289	1 ⊢ ℝ ≠ ∅

This proof depends on syntax axioms:   ≠ wne 2955  ∅c0 4277  ℝcr 11204  0cc0 11205

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732  ax-1cn 11263  ax-addrcl 11266  ax-rnegex 11276  ax-cnre 11278

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-ne 2956  df-rex 3087  df-dif 4046  df-nul 4278

This theorem is used by:  limsup0  46811  limsuppnfdlem  46818  limsup10ex  46890  liminf10ex  46891