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Mathbox for Glauco Siliprandi |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > ren0 | Structured version Visualization version GIF version |
Description: The set of reals is nonempty. (Contributed by Glauco Siliprandi, 23-Oct-2021.) |
Ref | Expression |
---|---|
ren0 | ⊢ ℝ ≠ ∅ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0re 11091 | . 2 ⊢ 0 ∈ ℝ | |
2 | 1 | ne0ii 4296 | 1 ⊢ ℝ ≠ ∅ |
Colors of variables: wff setvar class |
Syntax hints: ≠ wne 2942 ∅c0 4281 ℝcr 10984 0cc0 10985 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2709 ax-1cn 11043 ax-addrcl 11046 ax-rnegex 11056 ax-cnre 11058 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-fal 1555 df-ex 1783 df-sb 2069 df-clab 2716 df-cleq 2730 df-clel 2816 df-ne 2943 df-rex 3073 df-dif 3912 df-nul 4282 |
This theorem is referenced by: limsup0 43726 limsuppnfdlem 43733 limsup10ex 43805 liminf10ex 43806 |
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