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Mirrors > Home > ILE Home > Th. List > djussxp | Unicode version |
Description: Disjoint union is a subset of a cross product. (Contributed by Stefan O'Rear, 21-Nov-2014.) |
Ref | Expression |
---|---|
djussxp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iunss 3698 | . 2 | |
2 | snssi 3508 | . . 3 | |
3 | ssv 2965 | . . 3 | |
4 | xpss12 4445 | . . 3 | |
5 | 2, 3, 4 | sylancl 392 | . 2 |
6 | 1, 5 | mprgbir 2379 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1393 cvv 2557 wss 2917 csn 3375 ciun 3657 cxp 4343 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-in 2924 df-ss 2931 df-sn 3381 df-iun 3659 df-opab 3819 df-xp 4351 |
This theorem is referenced by: djudisj 4750 |
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