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Mirrors > Home > ILE Home > Th. List > undifss | Unicode version |
Description: Union of complementary parts into whole. (Contributed by Jim Kingdon, 4-Aug-2018.) |
Ref | Expression |
---|---|
undifss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | difss 3233 | . . . 4 | |
2 | 1 | jctr 313 | . . 3 |
3 | unss 3281 | . . 3 | |
4 | 2, 3 | sylib 121 | . 2 |
5 | ssun1 3270 | . . 3 | |
6 | sstr 3136 | . . 3 | |
7 | 5, 6 | mpan 421 | . 2 |
8 | 4, 7 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 cdif 3099 cun 3100 wss 3102 |
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 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 |
This theorem is referenced by: difsnss 3702 exmidundif 4167 exmidundifim 4168 undifdcss 6867 |
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