New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > snidg | Unicode version |
Description: A set is a member of its singleton. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 28-Oct-2003.) |
Ref | Expression |
---|---|
snidg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2353 | . 2 | |
2 | elsncg 3755 | . 2 | |
3 | 1, 2 | mpbiri 224 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1642 wcel 1710 csn 3737 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 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: snidb 3759 elsnc2g 3761 snnzg 3833 opkth1g 4130 fvunsn 5444 nchoicelem6 6294 dmfrec 6316 frec0 6321 |
Copyright terms: Public domain | W3C validator |