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Mirrors > Home > ILE Home > Th. List > caovdir2d | Unicode version |
Description: Convert an operation distributive law to class notation. (Contributed by Mario Carneiro, 30-Dec-2014.) |
Ref | Expression |
---|---|
caovdir2d.1 | |
caovdir2d.2 | |
caovdir2d.3 | |
caovdir2d.4 | |
caovdir2d.cl | |
caovdir2d.com |
Ref | Expression |
---|---|
caovdir2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovdir2d.1 | . . 3 | |
2 | caovdir2d.4 | . . 3 | |
3 | caovdir2d.2 | . . 3 | |
4 | caovdir2d.3 | . . 3 | |
5 | 1, 2, 3, 4 | caovdid 5946 | . 2 |
6 | caovdir2d.com | . . 3 | |
7 | caovdir2d.cl | . . . 4 | |
8 | 7, 3, 4 | caovcld 5924 | . . 3 |
9 | 6, 8, 2 | caovcomd 5927 | . 2 |
10 | 6, 3, 2 | caovcomd 5927 | . . 3 |
11 | 6, 4, 2 | caovcomd 5927 | . . 3 |
12 | 10, 11 | oveq12d 5792 | . 2 |
13 | 5, 9, 12 | 3eqtr4d 2182 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 962 wceq 1331 wcel 1480 (class class class)co 5774 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-iota 5088 df-fv 5131 df-ov 5777 |
This theorem is referenced by: addcmpblnq 7175 ltanqg 7208 addcmpblnq0 7251 mulasssrg 7566 mulgt0sr 7586 mulextsr1lem 7588 |
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