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Theorem pnrmtop 17169
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 17168 . 2  |-  ( J  e. PNrm  ->  J  e.  Nrm )
2 nrmtop 17164 . 2  |-  ( J  e.  Nrm  ->  J  e.  Top )
31, 2syl 15 1  |-  ( J  e. PNrm  ->  J  e.  Top )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1710   Topctop 16731   Nrmcnrm 17138  PNrmcpnrm 17140
This theorem is referenced by:  pnrmopn  17171
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ral 2624  df-rex 2625  df-rab 2628  df-v 2866  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-nul 3532  df-if 3642  df-sn 3722  df-pr 3723  df-op 3725  df-uni 3907  df-br 4103  df-opab 4157  df-mpt 4158  df-cnv 4776  df-dm 4778  df-rn 4779  df-iota 5298  df-fv 5342  df-ov 5945  df-nrm 17145  df-pnrm 17147
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