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Theorem ispnrm 17395
 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 5720 . . 3
2 oveq1 6080 . . . . 5
32mpteq1d 4282 . . . 4
43rneqd 5089 . . 3
51, 4sseq12d 3369 . 2
6 df-pnrm 17375 . 2 PNrm
75, 6elrab2 3086 1 PNrm
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wceq 1652   wcel 1725   wss 3312  cint 4042   cmpt 4258   crn 4871  cfv 5446  (class class class)co 6073   cmap 7010  cn 9992  ccld 17072  cnrm 17366  PNrmcpnrm 17368 This theorem is referenced by:  pnrmnrm  17396  pnrmcld  17398 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 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-cnv 4878  df-dm 4880  df-rn 4881  df-iota 5410  df-fv 5454  df-ov 6076  df-pnrm 17375
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