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Mirrors > Home > ILE Home > Th. List > elelsuc | Unicode version |
Description: Membership in a successor. (Contributed by NM, 20-Jun-1998.) |
Ref | Expression |
---|---|
elelsuc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 674 |
. 2
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2 | elsucg 4264 |
. 2
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3 | 1, 2 | mpbird 166 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 |
This theorem depends on definitions: df-bi 116 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-v 2643 df-un 3025 df-sn 3480 df-suc 4231 |
This theorem is referenced by: suctr 4281 ordsuc 4416 nnaordex 6353 fiintim 6746 exmidfodomrlemr 6967 exmidfodomrlemrALT 6968 ennnfonelemex 11719 |
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