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Mirrors > Home > ILE Home > Th. List > caovdi | Unicode version |
Description: Convert an operation distributive law to class notation. (Contributed by NM, 25-Aug-1995.) (Revised by Mario Carneiro, 28-Jun-2013.) |
Ref | Expression |
---|---|
caovdi.1 | |
caovdi.2 | |
caovdi.3 | |
caovdi.4 |
Ref | Expression |
---|---|
caovdi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovdi.1 | . 2 | |
2 | caovdi.2 | . 2 | |
3 | caovdi.3 | . 2 | |
4 | tru 1335 | . . 3 | |
5 | caovdi.4 | . . . . 5 | |
6 | 5 | a1i 9 | . . . 4 |
7 | 6 | caovdig 5945 | . . 3 |
8 | 4, 7 | mpan 420 | . 2 |
9 | 1, 2, 3, 8 | mp3an 1315 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 w3a 962 wceq 1331 wtru 1332 wcel 1480 cvv 2686 (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: (None) |
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