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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 5653 | . 2 |
6 | 1, 2, 3, 5 | syl12anc 1133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wcel 1393 (class class class)co 5512 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-iota 4867 df-fv 4910 df-ov 5515 |
This theorem is referenced by: caovdir2d 5677 caov4d 5685 caovdilemd 5692 caovlem2d 5693 grprinvd 5696 ecopovtrn 6203 ecopovtrng 6206 ordpipqqs 6472 ltanqg 6498 ltmnqg 6499 recexprlem1ssu 6732 mulgt0sr 6862 mulextsr1lem 6864 axmulass 6947 frec2uzrdg 9195 frecuzrdgsuc 9201 iseqovex 9219 iseqval 9220 iseqp1 9225 iseqdistr 9249 climcn2 9830 |
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