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Mirrors > Home > ILE Home > Th. List > unssbd | Unicode version |
Description: If is contained in , so is . One-way deduction form of unss 3281. Partial converse of unssd 3283. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
unssad.1 |
Ref | Expression |
---|---|
unssbd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unssad.1 | . . 3 | |
2 | unss 3281 | . . 3 | |
3 | 1, 2 | sylibr 133 | . 2 |
4 | 3 | simprd 113 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 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-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-un 3106 df-in 3108 df-ss 3115 |
This theorem is referenced by: eldifpw 4437 ertr 6495 diffifi 6839 sumsplitdc 11329 fsum2dlemstep 11331 fsumabs 11362 fsumiun 11374 fprod2dlemstep 11519 |
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