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Mirrors > Home > ILE Home > Th. List > iunsuc | Unicode version |
Description: Inductive definition for the indexed union at a successor. (Contributed by Mario Carneiro, 4-Feb-2013.) (Proof shortened by Mario Carneiro, 18-Nov-2016.) |
Ref | Expression |
---|---|
iunsuc.1 | |
iunsuc.2 |
Ref | Expression |
---|---|
iunsuc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-suc 4126 | . . 3 | |
2 | iuneq1 3691 | . . 3 | |
3 | 1, 2 | ax-mp 7 | . 2 |
4 | iunxun 3756 | . 2 | |
5 | iunsuc.1 | . . . 4 | |
6 | iunsuc.2 | . . . 4 | |
7 | 5, 6 | iunxsn 3754 | . . 3 |
8 | 7 | uneq2i 3123 | . 2 |
9 | 3, 4, 8 | 3eqtri 2105 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 wcel 1433 cvv 2601 cun 2971 csn 3398 ciun 3678 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-3an 921 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-rex 2354 df-v 2603 df-sbc 2816 df-un 2977 df-in 2979 df-ss 2986 df-sn 3404 df-iun 3680 df-suc 4126 |
This theorem is referenced by: (None) |
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