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Mirrors > Home > ILE Home > Th. List > caovassg | Unicode version |
Description: Convert an operation associative law to class notation. (Contributed by Mario Carneiro, 1-Jun-2013.) (Revised by Mario Carneiro, 26-May-2014.) |
Ref | Expression |
---|---|
caovassg.1 |
Ref | Expression |
---|---|
caovassg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovassg.1 | . . 3 | |
2 | 1 | ralrimivvva 2518 | . 2 |
3 | oveq1 5789 | . . . . 5 | |
4 | 3 | oveq1d 5797 | . . . 4 |
5 | oveq1 5789 | . . . 4 | |
6 | 4, 5 | eqeq12d 2155 | . . 3 |
7 | oveq2 5790 | . . . . 5 | |
8 | 7 | oveq1d 5797 | . . . 4 |
9 | oveq1 5789 | . . . . 5 | |
10 | 9 | oveq2d 5798 | . . . 4 |
11 | 8, 10 | eqeq12d 2155 | . . 3 |
12 | oveq2 5790 | . . . 4 | |
13 | oveq2 5790 | . . . . 5 | |
14 | 13 | oveq2d 5798 | . . . 4 |
15 | 12, 14 | eqeq12d 2155 | . . 3 |
16 | 6, 11, 15 | rspc3v 2809 | . 2 |
17 | 2, 16 | mpan9 279 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 963 wceq 1332 wcel 1481 wral 2417 (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: caovassd 5938 caovass 5939 grprinvlem 5973 grprinvd 5974 grpridd 5975 seq3split 10283 seq3caopr 10287 |
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