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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 4108 | . . 3 | |
2 | iuneq1 3670 | . . 3 | |
3 | 1, 2 | ax-mp 7 | . 2 |
4 | iunxun 3735 | . 2 | |
5 | iunsuc.1 | . . . 4 | |
6 | iunsuc.2 | . . . 4 | |
7 | 5, 6 | iunxsn 3733 | . . 3 |
8 | 7 | uneq2i 3094 | . 2 |
9 | 3, 4, 8 | 3eqtri 2064 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1243 wcel 1393 cvv 2557 cun 2915 csn 3375 ciun 3657 csuc 4102 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-sbc 2765 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-iun 3659 df-suc 4108 |
This theorem is referenced by: (None) |
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