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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 4320 | . 2 | |
2 | trss 4030 | . . 3 | |
3 | eqimss 3146 | . . . 4 | |
4 | 3 | a1i 9 | . . 3 |
5 | 2, 4 | jaod 706 | . 2 |
6 | 1, 5 | syl5 32 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wo 697 wceq 1331 wcel 1480 wss 3066 wtr 4021 csuc 4282 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-sn 3528 df-uni 3732 df-tr 4022 df-suc 4288 |
This theorem is referenced by: onsucsssucr 4420 ordpwsucss 4477 bj-el2oss1o 12970 nnsf 13188 nninfalllemn 13191 |
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