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Theorem pnrmtop 17436
Description: A perfectly normal space is a topological space. (Contributed by Mario Carneiro, 26-Aug-2015.)
Assertion
Ref Expression
pnrmtop  |-  ( J  e. PNrm  ->  J  e.  Top )

Proof of Theorem pnrmtop
StepHypRef Expression
1 pnrmnrm 17435 . 2  |-  ( J  e. PNrm  ->  J  e.  Nrm )
2 nrmtop 17431 . 2  |-  ( J  e.  Nrm  ->  J  e.  Top )
31, 2syl 16 1  |-  ( J  e. PNrm  ->  J  e.  Top )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1727   Topctop 16989   Nrmcnrm 17405  PNrmcpnrm 17407
This theorem is referenced by:  pnrmopn  17438
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423
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 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ral 2716  df-rex 2717  df-rab 2720  df-v 2964  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-uni 4040  df-br 4238  df-opab 4292  df-mpt 4293  df-cnv 4915  df-dm 4917  df-rn 4918  df-iota 5447  df-fv 5491  df-ov 6113  df-nrm 17412  df-pnrm 17414
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