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Mirrors > Home > ILE Home > Th. List > caovcl | Unicode version |
Description: Convert an operation closure law to class notation. (Contributed by NM, 4-Aug-1995.) (Revised by Mario Carneiro, 26-May-2014.) |
Ref | Expression |
---|---|
caovcl.1 |
Ref | Expression |
---|---|
caovcl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1335 | . 2 | |
2 | caovcl.1 | . . . 4 | |
3 | 2 | adantl 275 | . . 3 |
4 | 3 | caovclg 5916 | . 2 |
5 | 1, 4 | mpan 420 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wtru 1332 wcel 1480 (class class class)co 5767 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-iota 5083 df-fv 5126 df-ov 5770 |
This theorem is referenced by: ecopovtrn 6519 ecopovtrng 6522 genpelvl 7313 genpelvu 7314 genpml 7318 genpmu 7319 genprndl 7322 genprndu 7323 genpassl 7325 genpassu 7326 genpassg 7327 expcllem 10297 |
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