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Mirrors > Home > ILE Home > Th. List > djudisj | Unicode version |
Description: Disjoint unions with disjoint index sets are disjoint. (Contributed by Stefan O'Rear, 21-Nov-2014.) |
Ref | Expression |
---|---|
djudisj |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | djussxp 4499 | . 2 | |
2 | incom 3158 | . . 3 | |
3 | djussxp 4499 | . . . 4 | |
4 | incom 3158 | . . . . 5 | |
5 | xpdisj1 4767 | . . . . 5 | |
6 | 4, 5 | syl5eq 2125 | . . . 4 |
7 | ssdisj 3300 | . . . 4 | |
8 | 3, 6, 7 | sylancr 405 | . . 3 |
9 | 2, 8 | syl5eq 2125 | . 2 |
10 | ssdisj 3300 | . 2 | |
11 | 1, 9, 10 | sylancr 405 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 cvv 2601 cin 2972 wss 2973 c0 3251 csn 3398 ciun 3678 cxp 4361 |
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-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-nul 3252 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-iun 3680 df-opab 3840 df-xp 4369 df-rel 4370 |
This theorem is referenced by: (None) |
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