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Theorem pnrmnrm 17404
 Description: A perfectly normal space is normal. (Contributed by Mario Carneiro, 26-Aug-2015.)
Assertion
Ref Expression
pnrmnrm PNrm

Proof of Theorem pnrmnrm
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ispnrm 17403 . 2 PNrm
21simplbi 447 1 PNrm
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1725   wss 3320  cint 4050   cmpt 4266   crn 4879  cfv 5454  (class class class)co 6081   cmap 7018  cn 10000  ccld 17080  cnrm 17374  PNrmcpnrm 17376 This theorem is referenced by:  pnrmtop  17405 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-mpt 4268  df-cnv 4886  df-dm 4888  df-rn 4889  df-iota 5418  df-fv 5462  df-ov 6084  df-pnrm 17383
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