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Theorem ispnrm 17067
 Description: The property of being perfectly normal. (Contributed by Mario Carneiro, 26-Aug-2015.)
Assertion
Ref Expression
ispnrm PNrm
Distinct variable group:   ,

Proof of Theorem ispnrm
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fveq2 5525 . . 3
2 oveq1 5865 . . . . 5
3 mpteq1 4100 . . . . 5
42, 3syl 15 . . . 4
54rneqd 4906 . . 3
61, 5sseq12d 3207 . 2
7 df-pnrm 17047 . 2 PNrm
86, 7elrab2 2925 1 PNrm
 Colors of variables: wff set class Syntax hints:   wb 176   wa 358   wceq 1623   wcel 1684   wss 3152  cint 3862   cmpt 4077   crn 4690  cfv 5255  (class class class)co 5858   cmap 6772  cn 9746  ccld 16753  cnrm 17038  PNrmcpnrm 17040 This theorem is referenced by:  pnrmnrm  17068  pnrmcld  17070 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-mpt 4079  df-cnv 4697  df-dm 4699  df-rn 4700  df-iota 5219  df-fv 5263  df-ov 5861  df-pnrm 17047
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