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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 5519 | . . . 4 | |
2 | oveq1 5519 | . . . 4 | |
3 | 1, 2 | breq12d 3777 | . . 3 |
4 | 3 | bibi2d 221 | . 2 |
5 | caovord.1 | . . 3 | |
6 | caovord.2 | . . 3 | |
7 | breq1 3767 | . . . . . 6 | |
8 | oveq2 5520 | . . . . . . 7 | |
9 | 8 | breq1d 3774 | . . . . . 6 |
10 | 7, 9 | bibi12d 224 | . . . . 5 |
11 | breq2 3768 | . . . . . 6 | |
12 | oveq2 5520 | . . . . . . 7 | |
13 | 12 | breq2d 3776 | . . . . . 6 |
14 | 11, 13 | bibi12d 224 | . . . . 5 |
15 | 10, 14 | sylan9bb 435 | . . . 4 |
16 | 15 | imbi2d 219 | . . 3 |
17 | caovord.3 | . . 3 | |
18 | 5, 6, 16, 17 | vtocl2 2609 | . 2 |
19 | 4, 18 | vtoclga 2619 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wcel 1393 cvv 2557 class class class wbr 3764 (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-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: caovord2 5673 caovord3 5674 |
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