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Mirrors > Home > ILE Home > Th. List > caovcld | Unicode version |
Description: Convert an operation closure law to class notation. (Contributed by Mario Carneiro, 30-Dec-2014.) |
Ref | Expression |
---|---|
caovclg.1 | |
caovcld.2 | |
caovcld.3 |
Ref | Expression |
---|---|
caovcld |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 | |
2 | caovcld.2 | . 2 | |
3 | caovcld.3 | . 2 | |
4 | caovclg.1 | . . 3 | |
5 | 4 | caovclg 5931 | . 2 |
6 | 1, 2, 3, 5 | syl12anc 1215 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1481 (class class class)co 5782 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-iota 5096 df-fv 5139 df-ov 5785 |
This theorem is referenced by: caovdir2d 5955 caov4d 5963 caovdilemd 5970 caovlem2d 5971 grprinvd 5974 ecopovtrn 6534 ecopovtrng 6537 ordpipqqs 7206 ltanqg 7232 ltmnqg 7233 recexprlem1ssu 7466 mulgt0sr 7610 mulextsr1lem 7612 axmulass 7705 frec2uzrdg 10213 frecuzrdgsuc 10218 frecuzrdgsuctlem 10227 iseqovex 10260 seq3val 10262 seqf 10265 seq3p1 10266 seqp1cd 10270 seq3clss 10271 seq3distr 10317 climcn2 11110 |
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