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Mirrors > Home > ILE Home > Th. List > snssd | Unicode version |
Description: The singleton of an element of a class is a subset of the class (deduction form). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) |
Ref | Expression |
---|---|
snssd.1 |
Ref | Expression |
---|---|
snssd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snssd.1 | . 2 | |
2 | snssg 3703 | . . 3 | |
3 | 1, 2 | syl 14 | . 2 |
4 | 1, 3 | mpbid 146 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wcel 2135 wss 3111 csn 3570 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-in 3117 df-ss 3124 df-sn 3576 |
This theorem is referenced by: pwntru 4172 ecinxp 6567 xpdom3m 6791 ac6sfi 6855 undifdc 6880 iunfidisj 6902 fidcenumlemr 6911 ssfii 6930 en2other2 7143 un0addcl 9138 un0mulcl 9139 fseq1p1m1 10019 fsumge1 11388 fprodsplit1f 11561 phicl2 12125 ennnfonelemhf1o 12289 rest0 12726 iscnp4 12765 cnconst2 12780 cnpdis 12789 txdis 12824 txdis1cn 12825 fsumcncntop 13103 dvef 13235 bj-omtrans 13679 pwtrufal 13718 |
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