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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 4679 | . 2 | |
2 | incom 3263 | . . 3 | |
3 | djussxp 4679 | . . . 4 | |
4 | incom 3263 | . . . . 5 | |
5 | xpdisj1 4958 | . . . . 5 | |
6 | 4, 5 | syl5eq 2182 | . . . 4 |
7 | ssdisj 3414 | . . . 4 | |
8 | 3, 6, 7 | sylancr 410 | . . 3 |
9 | 2, 8 | syl5eq 2182 | . 2 |
10 | ssdisj 3414 | . 2 | |
11 | 1, 9, 10 | sylancr 410 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 cvv 2681 cin 3065 wss 3066 c0 3358 csn 3522 ciun 3808 cxp 4532 |
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-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-nul 3359 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-iun 3810 df-opab 3985 df-xp 4540 df-rel 4541 |
This theorem is referenced by: (None) |
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