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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 3824 | . 2 | |
2 | snssi 3634 | . . 3 | |
3 | ssv 3089 | . . 3 | |
4 | xpss12 4616 | . . 3 | |
5 | 2, 3, 4 | sylancl 409 | . 2 |
6 | 1, 5 | mprgbir 2467 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1465 cvv 2660 wss 3041 csn 3497 ciun 3783 cxp 4507 |
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-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-in 3047 df-ss 3054 df-sn 3503 df-iun 3785 df-opab 3960 df-xp 4515 |
This theorem is referenced by: djudisj 4936 |
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