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Mirrors > Home > ILE Home > Th. List > caovdig | Unicode version |
Description: Convert an operation distributive law to class notation. (Contributed by NM, 25-Aug-1995.) (Revised by Mario Carneiro, 26-Jul-2014.) |
Ref | Expression |
---|---|
caovdig.1 |
Ref | Expression |
---|---|
caovdig |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovdig.1 | . . 3 | |
2 | 1 | ralrimivvva 2513 | . 2 |
3 | oveq1 5774 | . . . 4 | |
4 | oveq1 5774 | . . . . 5 | |
5 | oveq1 5774 | . . . . 5 | |
6 | 4, 5 | oveq12d 5785 | . . . 4 |
7 | 3, 6 | eqeq12d 2152 | . . 3 |
8 | oveq1 5774 | . . . . 5 | |
9 | 8 | oveq2d 5783 | . . . 4 |
10 | oveq2 5775 | . . . . 5 | |
11 | 10 | oveq1d 5782 | . . . 4 |
12 | 9, 11 | eqeq12d 2152 | . . 3 |
13 | oveq2 5775 | . . . . 5 | |
14 | 13 | oveq2d 5783 | . . . 4 |
15 | oveq2 5775 | . . . . 5 | |
16 | 15 | oveq2d 5783 | . . . 4 |
17 | 14, 16 | eqeq12d 2152 | . . 3 |
18 | 7, 12, 17 | rspc3v 2800 | . 2 |
19 | 2, 18 | mpan9 279 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 962 wceq 1331 wcel 1480 wral 2414 (class class class)co 5767 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-iota 5083 df-fv 5126 df-ov 5770 |
This theorem is referenced by: caovdid 5939 caovdi 5943 |
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