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Theorem perflp 17220
Description: The limit points of a perfect space. (Contributed by Mario Carneiro, 24-Dec-2016.)
Hypothesis
Ref Expression
lpfval.1  |-  X  = 
U. J
Assertion
Ref Expression
perflp  |-  ( J  e. Perf  ->  ( ( limPt `  J ) `  X
)  =  X )

Proof of Theorem perflp
StepHypRef Expression
1 lpfval.1 . . 3  |-  X  = 
U. J
21isperf 17217 . 2  |-  ( J  e. Perf 
<->  ( J  e.  Top  /\  ( ( limPt `  J
) `  X )  =  X ) )
32simprbi 452 1  |-  ( J  e. Perf  ->  ( ( limPt `  J ) `  X
)  =  X )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1653    e. wcel 1726   U.cuni 4017   ` cfv 5456   Topctop 16960   limPtclp 17200  Perfcperf 17201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-iota 5420  df-fv 5464  df-perf 17203
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