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Mirrors > Home > NFE Home > Th. List > snid | Unicode version |
Description: A set is a member of its singleton. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 31-Dec-1993.) |
Ref | Expression |
---|---|
snid.1 |
Ref | Expression |
---|---|
snid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snid.1 | . 2 | |
2 | snidb 3759 | . 2 | |
3 | 1, 2 | mpbi 199 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wcel 1710 cvv 2859 csn 3737 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-sn 3741 |
This theorem is referenced by: rabsnt 3797 sneqr 3872 unsneqsn 3887 unipw 4117 eqpw1uni 4330 pw1eqadj 4332 0nelsuc 4400 0cnsuc 4401 nnsucelr 4428 nndisjeq 4429 ssfin 4470 eqtfinrelk 4486 0ceven 4505 vfinspss 4551 proj1op 4600 proj2op 4601 fsn 5432 fsn2 5434 fnressn 5438 fressnfv 5439 fvsn 5445 fvsnun1 5447 dmep 5524 map0 6025 mapsn 6026 xpsnen 6049 enadj 6060 2p1e3c 6156 frecxp 6314 |
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