Theorem ren0 45396

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 11242	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4324	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2933  ∅c0 4313  ℝcr 11133  0cc0 11134

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2708  ax-1cn 11192  ax-addrcl 11195  ax-rnegex 11205  ax-cnre 11207

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2715  df-cleq 2728  df-clel 2810  df-ne 2934  df-rex 3062  df-dif 3934  df-nul 4314

This theorem is referenced by:  limsup0  45690  limsuppnfdlem  45697  limsup10ex  45769  liminf10ex  45770