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Mirrors > Home > ILE Home > Th. List > snm | Unicode version |
Description: The singleton of a set is inhabited. (Contributed by Jim Kingdon, 11-Aug-2018.) |
Ref | Expression |
---|---|
snnz.1 |
Ref | Expression |
---|---|
snm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snnz.1 | . 2 | |
2 | snmg 3699 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wex 1485 wcel 2141 cvv 2730 csn 3581 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-sn 3587 |
This theorem is referenced by: mss 4209 ssfilem 6851 diffitest 6863 djuexb 7019 exmidonfinlem 7163 exmidfodomrlemim 7171 cc2lem 7221 |
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