Theorem ren0 42615

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 10835	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4252	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2940  ∅c0 4237  ℝcr 10728  0cc0 10729

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-ext 2708  ax-1cn 10787  ax-addrcl 10790  ax-rnegex 10800  ax-cnre 10802

This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1546  df-fal 1556  df-ex 1788  df-sb 2071  df-clab 2715  df-cleq 2729  df-clel 2816  df-ne 2941  df-ral 3066  df-rex 3067  df-dif 3869  df-nul 4238

This theorem is referenced by:  limsup0  42910  limsuppnfdlem  42917  limsup10ex  42989  liminf10ex  42990