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Mirrors > Home > ILE Home > Th. List > unssad | Unicode version |
Description: If is contained in , so is . One-way deduction form of unss 3255. Partial converse of unssd 3257. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
unssad.1 |
Ref | Expression |
---|---|
unssad |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unssad.1 | . . 3 | |
2 | unss 3255 | . . 3 | |
3 | 1, 2 | sylibr 133 | . 2 |
4 | 3 | simpld 111 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 cun 3074 wss 3076 |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 |
This theorem is referenced by: ersym 6449 findcard2d 6793 findcard2sd 6794 diffifi 6796 sumsplitdc 11233 fsumabs 11266 fsumiun 11278 |
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