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Mirrors > Home > ILE Home > Th. List > difundi | Unicode version |
Description: Distributive law for class difference. Theorem 39 of [Suppes] p. 29. (Contributed by NM, 17-Aug-2004.) |
Ref | Expression |
---|---|
difundi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldif 3080 | . . . 4 | |
2 | eldif 3080 | . . . 4 | |
3 | 1, 2 | anbi12i 455 | . . 3 |
4 | elin 3259 | . . 3 | |
5 | eldif 3080 | . . . . . 6 | |
6 | elun 3217 | . . . . . . . 8 | |
7 | 6 | notbii 657 | . . . . . . 7 |
8 | 7 | anbi2i 452 | . . . . . 6 |
9 | 5, 8 | bitri 183 | . . . . 5 |
10 | ioran 741 | . . . . . 6 | |
11 | 10 | anbi2i 452 | . . . . 5 |
12 | 9, 11 | bitri 183 | . . . 4 |
13 | anandi 579 | . . . 4 | |
14 | 12, 13 | bitri 183 | . . 3 |
15 | 3, 4, 14 | 3bitr4ri 212 | . 2 |
16 | 15 | eqriv 2136 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wo 697 wceq 1331 wcel 1480 cdif 3068 cun 3069 cin 3070 |
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-in1 603 ax-in2 604 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-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-dif 3073 df-un 3075 df-in 3077 |
This theorem is referenced by: undm 3334 undifdc 6812 uncld 12282 |
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