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Mirrors > Home > ILE Home > Th. List > elsuc2g | Unicode version |
Description: Variant of membership in a successor, requiring that rather than be a set. (Contributed by NM, 28-Oct-2003.) |
Ref | Expression |
---|---|
elsuc2g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-suc 4343 | . . 3 | |
2 | 1 | eleq2i 2231 | . 2 |
3 | elun 3258 | . . 3 | |
4 | elsn2g 3603 | . . . 4 | |
5 | 4 | orbi2d 780 | . . 3 |
6 | 3, 5 | syl5bb 191 | . 2 |
7 | 2, 6 | syl5bb 191 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wo 698 wceq 1342 wcel 2135 cun 3109 csn 3570 csuc 4337 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-un 3115 df-sn 3576 df-suc 4343 |
This theorem is referenced by: elsuc2 4379 nntri3or 6452 frec2uzltd 10328 |
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