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Mirrors > Home > ILE Home > Th. List > suc0 | Unicode version |
Description: The successor of the empty set. (Contributed by NM, 1-Feb-2005.) |
Ref | Expression |
---|---|
suc0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-suc 4293 | . 2 | |
2 | uncom 3220 | . 2 | |
3 | un0 3396 | . 2 | |
4 | 1, 2, 3 | 3eqtri 2164 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 cun 3069 c0 3363 csn 3527 csuc 4287 |
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-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-dif 3073 df-un 3075 df-nul 3364 df-suc 4293 |
This theorem is referenced by: ordtriexmidlem 4435 ordtri2orexmid 4438 2ordpr 4439 onsucsssucexmid 4442 onsucelsucexmid 4445 ordsoexmid 4477 ordtri2or2exmid 4486 nnregexmid 4534 omsinds 4535 tfr0dm 6219 df1o2 6326 nninfsellemdc 13206 |
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