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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 3626 | . . 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 1465 wss 3041 csn 3497 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-in 3047 df-ss 3054 df-sn 3503 |
This theorem is referenced by: pwntru 4092 ecinxp 6472 xpdom3m 6696 ac6sfi 6760 undifdc 6780 iunfidisj 6802 fidcenumlemr 6811 ssfii 6830 en2other2 7020 un0addcl 8978 un0mulcl 8979 fseq1p1m1 9842 fsumge1 11198 phicl2 11817 ennnfonelemhf1o 11853 rest0 12275 iscnp4 12314 cnconst2 12329 cnpdis 12338 txdis 12373 txdis1cn 12374 fsumcncntop 12652 dvef 12783 bj-omtrans 13081 pwtrufal 13119 |
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