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Theorem pnrmtop 17367
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 17366 . 2  |-  ( J  e. PNrm  ->  J  e.  Nrm )
2 nrmtop 17362 . 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 1721   Topctop 16921   Nrmcnrm 17336  PNrmcpnrm 17338
This theorem is referenced by:  pnrmopn  17369
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-ral 2679  df-rex 2680  df-rab 2683  df-v 2926  df-dif 3291  df-un 3293  df-in 3295  df-ss 3302  df-nul 3597  df-if 3708  df-sn 3788  df-pr 3789  df-op 3791  df-uni 3984  df-br 4181  df-opab 4235  df-mpt 4236  df-cnv 4853  df-dm 4855  df-rn 4856  df-iota 5385  df-fv 5429  df-ov 6051  df-nrm 17343  df-pnrm 17345
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