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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 2417 |
. 2
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2 | dfcleq 2089 |
. . . 4
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3 | vex 2636 |
. . . . . . 7
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4 | 3 | elsuc 4257 |
. . . . . 6
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5 | 4 | bibi2i 226 |
. . . . 5
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6 | 5 | albii 1411 |
. . . 4
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7 | 2, 6 | bitri 183 |
. . 3
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8 | 7 | rexbii 2396 |
. 2
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9 | 1, 8 | bitri 183 |
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 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 |
This theorem depends on definitions: df-bi 116 df-tru 1299 df-nf 1402 df-sb 1700 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-rex 2376 df-v 2635 df-un 3017 df-sn 3472 df-suc 4222 |
This theorem is referenced by: (None) |
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