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Mirrors > Home > ILE Home > Th. List > sucel | Unicode version |
Description: Membership of a successor in another class. (Contributed by NM, 29-Jun-2004.) |
Ref | Expression |
---|---|
sucel |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | risset 2402 |
. 2
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2 | dfcleq 2079 |
. . . 4
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3 | vex 2617 |
. . . . . . 7
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4 | 3 | elsuc 4200 |
. . . . . 6
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5 | 4 | bibi2i 225 |
. . . . 5
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6 | 5 | albii 1402 |
. . . 4
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7 | 2, 6 | bitri 182 |
. . 3
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8 | 7 | rexbii 2381 |
. 2
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9 | 1, 8 | bitri 182 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1379 ax-7 1380 ax-gen 1381 ax-ie1 1425 ax-ie2 1426 ax-8 1438 ax-10 1439 ax-11 1440 ax-i12 1441 ax-bndl 1442 ax-4 1443 ax-17 1462 ax-i9 1466 ax-ial 1470 ax-i5r 1471 ax-ext 2067 |
This theorem depends on definitions: df-bi 115 df-tru 1290 df-nf 1393 df-sb 1690 df-clab 2072 df-cleq 2078 df-clel 2081 df-nfc 2214 df-rex 2361 df-v 2616 df-un 2990 df-sn 3431 df-suc 4165 |
This theorem is referenced by: (None) |
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