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Theorem isperf 17215
 Description: Definition of a perfect space. (Contributed by Mario Carneiro, 24-Dec-2016.)
Hypothesis
Ref Expression
lpfval.1
Assertion
Ref Expression
isperf Perf

Proof of Theorem isperf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fveq2 5728 . . . 4
2 unieq 4024 . . . . 5
3 lpfval.1 . . . . 5
42, 3syl6eqr 2486 . . . 4
51, 4fveq12d 5734 . . 3
65, 4eqeq12d 2450 . 2
7 df-perf 17201 . 2 Perf
86, 7elrab2 3094 1 Perf
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wceq 1652   wcel 1725  cuni 4015  cfv 5454  ctop 16958  clp 17198  Perfcperf 17199 This theorem is referenced by:  isperf2  17216  perflp  17218  perftop  17220  restperf  17248 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-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-iota 5418  df-fv 5462  df-perf 17201
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