Theorem ren0 46381

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 11303	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4290	1 ⊢ ℝ ≠ ∅

This proof depends on syntax axioms:   ≠ wne 2956  ∅c0 4279  ℝcr 11192  0cc0 11193

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2733  ax-1cn 11251  ax-addrcl 11254  ax-rnegex 11264  ax-cnre 11266

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2740  df-cleq 2753  df-clel 2836  df-ne 2957  df-rex 3088  df-dif 3902  df-nul 4280

This theorem is used by:  limsup0  46673  limsuppnfdlem  46680  limsup10ex  46752  liminf10ex  46753