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Mirrors > Home > ILE Home > Th. List > snssi | Unicode version |
Description: The singleton of an element of a class is a subset of the class. (Contributed by NM, 6-Jun-1994.) |
Ref | Expression |
---|---|
snssi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snssg 3716 | . 2 | |
2 | 1 | ibi 175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2141 wss 3121 csn 3583 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-in 3127 df-ss 3134 df-sn 3589 |
This theorem is referenced by: difsnss 3726 sssnm 3741 tpssi 3746 snelpwi 4197 intid 4209 abnexg 4431 ordsucss 4488 xpsspw 4723 djussxp 4756 xpimasn 5059 fconst6g 5396 f1sng 5484 fvimacnvi 5610 fsn2 5670 fnressn 5682 fsnunf 5696 mapsn 6668 unsnfidcel 6898 en1eqsn 6925 exmidfodomrlemim 7178 axresscn 7822 nn0ssre 9139 1fv 10095 fxnn0nninf 10394 1exp 10505 hashdifsn 10754 hashdifpr 10755 fsum00 11425 hash2iun1dif1 11443 exmidunben 12381 isneip 12940 neipsm 12948 opnneip 12953 |
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