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Theorem perftop 18902
Description: A perfect space is a topology. (Contributed by Mario Carneiro, 25-Dec-2016.)
Assertion
Ref Expression
perftop  |-  ( J  e. Perf  ->  J  e.  Top )

Proof of Theorem perftop
StepHypRef Expression
1 eqid 2454 . . 3  |-  U. J  =  U. J
21isperf 18897 . 2  |-  ( J  e. Perf 
<->  ( J  e.  Top  /\  ( ( limPt `  J
) `  U. J )  =  U. J ) )
32simplbi 460 1  |-  ( J  e. Perf  ->  J  e.  Top )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1370    e. wcel 1758   U.cuni 4202   ` cfv 5529   Topctop 18640   limPtclp 18880  Perfcperf 18881
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-rex 2805  df-rab 2808  df-v 3080  df-dif 3442  df-un 3444  df-in 3446  df-ss 3453  df-nul 3749  df-if 3903  df-sn 3989  df-pr 3991  df-op 3995  df-uni 4203  df-br 4404  df-iota 5492  df-fv 5537  df-perf 18883
This theorem is referenced by:  perfopn  18931
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