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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 22347 | . 2 β’ (π½ β Perf β (π½ β Top β§ ((limPtβπ½)βπ) = π)) |
3 | 2 | simprbi 498 | 1 β’ (π½ β Perf β ((limPtβπ½)βπ) = π) |
Colors of variables: wff setvar class |
Syntax hints: β wi 4 = wceq 1539 β wcel 2104 βͺ cuni 4844 βcfv 6458 Topctop 22087 limPtclp 22330 Perfcperf 22331 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1911 ax-6 1969 ax-7 2009 ax-8 2106 ax-9 2114 ax-ext 2707 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 846 df-3an 1089 df-tru 1542 df-fal 1552 df-ex 1780 df-sb 2066 df-clab 2714 df-cleq 2728 df-clel 2814 df-rab 3287 df-v 3439 df-dif 3895 df-un 3897 df-in 3899 df-ss 3909 df-nul 4263 df-if 4466 df-sn 4566 df-pr 4568 df-op 4572 df-uni 4845 df-br 5082 df-iota 6410 df-fv 6466 df-perf 22333 |
This theorem is referenced by: (None) |
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