Theorem ren0 46116

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 11205	. 2 ⊢ 0 ∈ ℝ
2	1	ne0ii 4297	1 ⊢ ℝ ≠ ∅

Syntax hints:   ≠ wne 2958  ∅c0 4286  ℝcr 11094  0cc0 11095

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735  ax-1cn 11153  ax-addrcl 11156  ax-rnegex 11166  ax-cnre 11168

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1573  df-fal 1583  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-ne 2959  df-rex 3090  df-dif 3908  df-nul 4287

This theorem is referenced by:  limsup0  46408  limsuppnfdlem  46415  limsup10ex  46487  liminf10ex  46488