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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 |
---|---|
snssd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snssd.1 |
. 2
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2 | snssg 3622 |
. . 3
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3 | 1, 2 | syl 14 |
. 2
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4 | 1, 3 | mpbid 146 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-v 2659 df-in 3043 df-ss 3050 df-sn 3499 |
This theorem is referenced by: pwntru 4082 ecinxp 6458 xpdom3m 6681 ac6sfi 6745 undifdc 6765 iunfidisj 6786 fidcenumlemr 6795 ssfii 6814 en2other2 7000 un0addcl 8914 un0mulcl 8915 fseq1p1m1 9767 fsumge1 11122 phicl2 11735 ennnfonelemhf1o 11771 rest0 12191 iscnp4 12229 cnconst2 12244 cnpdis 12253 txdis 12288 txdis1cn 12289 fsumcncntop 12542 bj-omtrans 12846 pwtrufal 12884 |
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