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Mirrors > Home > ILE Home > Th. List > caovdirg | Unicode version |
Description: Convert an operation reverse distributive law to class notation. (Contributed by Mario Carneiro, 19-Oct-2014.) |
Ref | Expression |
---|---|
caovdirg.1 |
Ref | Expression |
---|---|
caovdirg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovdirg.1 | . . 3 | |
2 | 1 | ralrimivvva 2540 | . 2 |
3 | oveq1 5831 | . . . . 5 | |
4 | 3 | oveq1d 5839 | . . . 4 |
5 | oveq1 5831 | . . . . 5 | |
6 | 5 | oveq1d 5839 | . . . 4 |
7 | 4, 6 | eqeq12d 2172 | . . 3 |
8 | oveq2 5832 | . . . . 5 | |
9 | 8 | oveq1d 5839 | . . . 4 |
10 | oveq1 5831 | . . . . 5 | |
11 | 10 | oveq2d 5840 | . . . 4 |
12 | 9, 11 | eqeq12d 2172 | . . 3 |
13 | oveq2 5832 | . . . 4 | |
14 | oveq2 5832 | . . . . 5 | |
15 | oveq2 5832 | . . . . 5 | |
16 | 14, 15 | oveq12d 5842 | . . . 4 |
17 | 13, 16 | eqeq12d 2172 | . . 3 |
18 | 7, 12, 17 | rspc3v 2832 | . 2 |
19 | 2, 18 | mpan9 279 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 963 wceq 1335 wcel 2128 wral 2435 (class class class)co 5824 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-iota 5135 df-fv 5178 df-ov 5827 |
This theorem is referenced by: caovdird 5999 caovlem2d 6013 |
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