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Mirrors > Home > ILE Home > Th. List > disj3 | Unicode version |
Description: Two ways of saying that two classes are disjoint. (Contributed by NM, 19-May-1998.) |
Ref | Expression |
---|---|
disj3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm4.71 381 | . . . 4 | |
2 | eldif 2982 | . . . . 5 | |
3 | 2 | bibi2i 225 | . . . 4 |
4 | 1, 3 | bitr4i 185 | . . 3 |
5 | 4 | albii 1399 | . 2 |
6 | disj1 3294 | . 2 | |
7 | dfcleq 2075 | . 2 | |
8 | 5, 6, 7 | 3bitr4i 210 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 wb 103 wal 1282 wceq 1284 wcel 1433 cdif 2970 cin 2972 c0 3251 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-v 2603 df-dif 2975 df-in 2979 df-nul 3252 |
This theorem is referenced by: disjel 3298 uneqdifeqim 3328 difprsn1 3525 diftpsn3 3527 orddif 4290 phpm 6351 |
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