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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 4263 | . . 3 | |
2 | iuneq1 3796 | . . 3 | |
3 | 1, 2 | ax-mp 5 | . 2 |
4 | iunxun 3862 | . 2 | |
5 | iunsuc.1 | . . . 4 | |
6 | iunsuc.2 | . . . 4 | |
7 | 5, 6 | iunxsn 3859 | . . 3 |
8 | 7 | uneq2i 3197 | . 2 |
9 | 3, 4, 8 | 3eqtri 2142 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 wcel 1465 cvv 2660 cun 3039 csn 3497 ciun 3783 csuc 4257 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-sbc 2883 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-iun 3785 df-suc 4263 |
This theorem is referenced by: (None) |
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