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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 2547 | . 2 |
3 | oveq1 5844 | . . . . 5 | |
4 | 3 | oveq1d 5852 | . . . 4 |
5 | oveq1 5844 | . . . 4 | |
6 | 4, 5 | eqeq12d 2179 | . . 3 |
7 | oveq2 5845 | . . . . 5 | |
8 | 7 | oveq1d 5852 | . . . 4 |
9 | oveq1 5844 | . . . . 5 | |
10 | 9 | oveq2d 5853 | . . . 4 |
11 | 8, 10 | eqeq12d 2179 | . . 3 |
12 | oveq2 5845 | . . . 4 | |
13 | oveq2 5845 | . . . . 5 | |
14 | 13 | oveq2d 5853 | . . . 4 |
15 | 12, 14 | eqeq12d 2179 | . . 3 |
16 | 6, 11, 15 | rspc3v 2842 | . 2 |
17 | 2, 16 | mpan9 279 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 967 wceq 1342 wcel 2135 wral 2442 (class class class)co 5837 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2724 df-un 3116 df-sn 3577 df-pr 3578 df-op 3580 df-uni 3785 df-br 3978 df-iota 5148 df-fv 5191 df-ov 5840 |
This theorem is referenced by: caovassd 5993 caovass 5994 grprinvlem 6028 grprinvd 6029 grpridd 6030 seq3split 10405 seq3caopr 10409 |
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