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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 4333 | . 2 | |
2 | uncom 3252 | . 2 | |
3 | un0 3428 | . 2 | |
4 | 1, 2, 3 | 3eqtri 2182 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1335 cun 3100 c0 3395 csn 3561 csuc 4327 |
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 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-v 2714 df-dif 3104 df-un 3106 df-nul 3396 df-suc 4333 |
This theorem is referenced by: ordtriexmidlem 4480 ordtri2orexmid 4484 2ordpr 4485 onsucsssucexmid 4488 onsucelsucexmid 4491 ordsoexmid 4523 ordtri2or2exmid 4532 ontri2orexmidim 4533 nnregexmid 4582 omsinds 4583 tfr0dm 6271 df1o2 6378 nninfsellemdc 13653 |
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