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Theorem isperf 19778
 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 5872 . . . 4
2 unieq 4259 . . . . 5
3 lpfval.1 . . . . 5
42, 3syl6eqr 2516 . . . 4
51, 4fveq12d 5878 . . 3
65, 4eqeq12d 2479 . 2
7 df-perf 19764 . 2 Perf
86, 7elrab2 3259 1 Perf
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369   wceq 1395   wcel 1819  cuni 4251  cfv 5594  ctop 19520  clp 19761  Perfcperf 19762 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-uni 4252  df-br 4457  df-iota 5557  df-fv 5602  df-perf 19764 This theorem is referenced by:  isperf2  19779  perflp  19781  perftop  19783  restperf  19811
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