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Mirrors > Home > ILE Home > Th. List > elsucg | Unicode version |
Description: Membership in a successor. Exercise 5 of [TakeutiZaring] p. 17. (Contributed by NM, 15-Sep-1995.) |
Ref | Expression |
---|---|
elsucg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-suc 4108 | . . . 4 | |
2 | 1 | eleq2i 2104 | . . 3 |
3 | elun 3084 | . . 3 | |
4 | 2, 3 | bitri 173 | . 2 |
5 | elsng 3390 | . . 3 | |
6 | 5 | orbi2d 704 | . 2 |
7 | 4, 6 | syl5bb 181 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wo 629 wceq 1243 wcel 1393 cun 2915 csn 3375 csuc 4102 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-sn 3381 df-suc 4108 |
This theorem is referenced by: elsuc 4143 elelsuc 4146 sucidg 4153 onsucelsucr 4234 onsucsssucexmid 4252 suc11g 4281 nlt1pig 6439 bj-peano4 10080 |
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