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Mirrors > Home > ILE Home > Th. List > trsucss | Unicode version |
Description: A member of the successor of a transitive class is a subclass of it. (Contributed by NM, 4-Oct-2003.) |
Ref | Expression |
---|---|
trsucss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elsuci 4158 | . 2 | |
2 | trss 3884 | . . 3 | |
3 | eqimss 3051 | . . . 4 | |
4 | 3 | a1i 9 | . . 3 |
5 | 2, 4 | jaod 669 | . 2 |
6 | 1, 5 | syl5 32 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wo 661 wceq 1284 wcel 1433 wss 2973 wtr 3875 csuc 4120 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-sn 3404 df-uni 3602 df-tr 3876 df-suc 4126 |
This theorem is referenced by: onsucsssucr 4253 ordpwsucss 4310 |
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