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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 5914 | . 2 |
6 | caovdir2d.com | . . 3 | |
7 | caovdir2d.cl | . . . 4 | |
8 | 7, 3, 4 | caovcld 5892 | . . 3 |
9 | 6, 8, 2 | caovcomd 5895 | . 2 |
10 | 6, 3, 2 | caovcomd 5895 | . . 3 |
11 | 6, 4, 2 | caovcomd 5895 | . . 3 |
12 | 10, 11 | oveq12d 5760 | . 2 |
13 | 5, 9, 12 | 3eqtr4d 2160 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 947 wceq 1316 wcel 1465 (class class class)co 5742 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-iota 5058 df-fv 5101 df-ov 5745 |
This theorem is referenced by: addcmpblnq 7143 ltanqg 7176 addcmpblnq0 7219 mulasssrg 7534 mulgt0sr 7554 mulextsr1lem 7556 |
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