Theorem ren0 45845

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 11137	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4272	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2934  ∅c0 4261  ℝcr 11028  0cc0 11029

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711  ax-1cn 11087  ax-addrcl 11090  ax-rnegex 11100  ax-cnre 11102

This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1550  df-fal 1560  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-ne 2935  df-rex 3064  df-dif 3886  df-nul 4262

This theorem is referenced by:  limsup0  46137  limsuppnfdlem  46144  limsup10ex  46216  liminf10ex  46217