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 10645 | . 2 ⊢ 0 ∈ ℝ | |
2 | 1 | ne0ii 4305 | 1 ⊢ ℝ ≠ ∅ |
Colors of variables: wff setvar class |
Syntax hints: ≠ wne 3018 ∅c0 4293 ℝcr 10538 0cc0 10539 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-ext 2795 ax-1cn 10597 ax-addrcl 10600 ax-rnegex 10610 ax-cnre 10612 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1781 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-ne 3019 df-ral 3145 df-rex 3146 df-dif 3941 df-nul 4294 |
This theorem is referenced by: limsup0 41982 limsuppnfdlem 41989 limsup10ex 42061 liminf10ex 42062 |
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