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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 |
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Ref | Expression |
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snssd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snssd.1 |
. 2
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2 | snssg 3741 |
. . 3
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3 | 1, 2 | syl 14 |
. 2
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4 | 1, 3 | mpbid 147 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 df-in 3150 df-ss 3157 df-sn 3613 |
This theorem is referenced by: pwntru 4217 ecinxp 6636 xpdom3m 6860 ac6sfi 6926 undifdc 6952 iunfidisj 6975 fidcenumlemr 6984 ssfii 7003 en2other2 7225 un0addcl 9239 un0mulcl 9240 fseq1p1m1 10124 fsumge1 11501 fprodsplit1f 11674 phicl2 12246 ennnfonelemhf1o 12464 imasaddfnlemg 12791 imasaddflemg 12793 0subm 12936 trivsubgd 13139 trivsubgsnd 13140 trivnsgd 13156 kerf1ghm 13213 lsssn0 13686 lss0ss 13687 lsptpcl 13710 lspsnvsi 13734 lspun0 13741 mulgrhm2 13908 rest0 14136 iscnp4 14175 cnconst2 14190 cnpdis 14199 txdis 14234 txdis1cn 14235 fsumcncntop 14513 dvef 14645 bj-omtrans 15166 pwtrufal 15206 |
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