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Mirrors > Home > MPE Home > Th. List > cfilfil | Structured version Unicode version |
Description: A Cauchy filter is a filter. (Contributed by Mario Carneiro, 13-Oct-2015.) |
Ref | Expression |
---|---|
cfilfil |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iscfil 20894 |
. 2
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2 | 1 | simprbda 623 |
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-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 ax-sep 4513 ax-nul 4521 ax-pow 4570 ax-pr 4631 ax-un 6474 ax-cnex 9441 ax-resscn 9442 |
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-eu 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-ral 2800 df-rex 2801 df-rab 2804 df-v 3072 df-sbc 3287 df-dif 3431 df-un 3433 df-in 3435 df-ss 3442 df-nul 3738 df-if 3892 df-pw 3962 df-sn 3978 df-pr 3980 df-op 3984 df-uni 4192 df-br 4393 df-opab 4451 df-mpt 4452 df-id 4736 df-xp 4946 df-rel 4947 df-cnv 4948 df-co 4949 df-dm 4950 df-rn 4951 df-res 4952 df-ima 4953 df-iota 5481 df-fun 5520 df-fn 5521 df-f 5522 df-fv 5526 df-ov 6195 df-oprab 6196 df-mpt2 6197 df-map 7318 df-xr 9525 df-xmet 17921 df-cfil 20884 |
This theorem is referenced by: cfil3i 20898 iscfil3 20902 cfilfcls 20903 iscmet3 20922 cfilresi 20924 cmetss 20943 relcmpcmet 20945 cfilucfil4OLD 20949 cfilucfil4 20950 fmcncfil 26497 |
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