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Mirrors > Home > MPE Home > Th. List > perflp | Structured version Visualization version GIF version |
Description: The limit points of a perfect space. (Contributed by Mario Carneiro, 24-Dec-2016.) |
Ref | Expression |
---|---|
lpfval.1 | β’ π = βͺ π½ |
Ref | Expression |
---|---|
perflp | β’ (π½ β Perf β ((limPtβπ½)βπ) = π) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lpfval.1 | . . 3 β’ π = βͺ π½ | |
2 | 1 | isperf 23006 | . 2 β’ (π½ β Perf β (π½ β Top β§ ((limPtβπ½)βπ) = π)) |
3 | 2 | simprbi 496 | 1 β’ (π½ β Perf β ((limPtβπ½)βπ) = π) |
Colors of variables: wff setvar class |
Syntax hints: β wi 4 = wceq 1533 β wcel 2098 βͺ cuni 4902 βcfv 6536 Topctop 22746 limPtclp 22989 Perfcperf 22990 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2697 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-sb 2060 df-clab 2704 df-cleq 2718 df-clel 2804 df-rab 3427 df-v 3470 df-dif 3946 df-un 3948 df-in 3950 df-ss 3960 df-nul 4318 df-if 4524 df-sn 4624 df-pr 4626 df-op 4630 df-uni 4903 df-br 5142 df-iota 6488 df-fv 6544 df-perf 22992 |
This theorem is referenced by: (None) |
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