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Mirrors > Home > MPE Home > Th. List > perftop | Structured version Unicode version |
Description: A perfect space is a topology. (Contributed by Mario Carneiro, 25-Dec-2016.) |
Ref | Expression |
---|---|
perftop |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2454 |
. . 3
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2 | 1 | isperf 18897 |
. 2
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3 | 2 | simplbi 460 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-rex 2805 df-rab 2808 df-v 3080 df-dif 3442 df-un 3444 df-in 3446 df-ss 3453 df-nul 3749 df-if 3903 df-sn 3989 df-pr 3991 df-op 3995 df-uni 4203 df-br 4404 df-iota 5492 df-fv 5537 df-perf 18883 |
This theorem is referenced by: perfopn 18931 |
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