Theorem ren0 45937

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 11177	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4294	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2956  ∅c0 4283  ℝcr 11066  0cc0 11067

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733  ax-1cn 11125  ax-addrcl 11128  ax-rnegex 11138  ax-cnre 11140

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1562  df-fal 1572  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-ne 2957  df-rex 3086  df-dif 3905  df-nul 4284

This theorem is referenced by:  limsup0  46229  limsuppnfdlem  46236  limsup10ex  46308  liminf10ex  46309