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Mirrors > Home > ILE Home > Th. List > caovord | Unicode version |
Description: Convert an operation ordering law to class notation. (Contributed by NM, 19-Feb-1996.) |
Ref | Expression |
---|---|
caovord.1 | |
caovord.2 | |
caovord.3 |
Ref | Expression |
---|---|
caovord |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1 5843 | . . . 4 | |
2 | oveq1 5843 | . . . 4 | |
3 | 1, 2 | breq12d 3989 | . . 3 |
4 | 3 | bibi2d 231 | . 2 |
5 | caovord.1 | . . 3 | |
6 | caovord.2 | . . 3 | |
7 | breq1 3979 | . . . . . 6 | |
8 | oveq2 5844 | . . . . . . 7 | |
9 | 8 | breq1d 3986 | . . . . . 6 |
10 | 7, 9 | bibi12d 234 | . . . . 5 |
11 | breq2 3980 | . . . . . 6 | |
12 | oveq2 5844 | . . . . . . 7 | |
13 | 12 | breq2d 3988 | . . . . . 6 |
14 | 11, 13 | bibi12d 234 | . . . . 5 |
15 | 10, 14 | sylan9bb 458 | . . . 4 |
16 | 15 | imbi2d 229 | . . 3 |
17 | caovord.3 | . . 3 | |
18 | 5, 6, 16, 17 | vtocl2 2776 | . 2 |
19 | 4, 18 | vtoclga 2787 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1342 wcel 2135 cvv 2721 class class class wbr 3976 (class class class)co 5836 |
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-rex 2448 df-v 2723 df-un 3115 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-iota 5147 df-fv 5190 df-ov 5839 |
This theorem is referenced by: caovord2 6005 caovord3 6006 |
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