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Mirrors > Home > ILE Home > Th. List > iunxsn | Unicode version |
Description: A singleton index picks out an instance of an indexed union's argument. (Contributed by NM, 26-Mar-2004.) (Proof shortened by Mario Carneiro, 25-Jun-2016.) |
Ref | Expression |
---|---|
iunxsn.1 | |
iunxsn.2 |
Ref | Expression |
---|---|
iunxsn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iunxsn.1 | . 2 | |
2 | iunxsn.2 | . . 3 | |
3 | 2 | iunxsng 3925 | . 2 |
4 | 1, 3 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 wcel 2128 cvv 2712 csn 3560 ciun 3850 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-sn 3566 df-iun 3852 |
This theorem is referenced by: iunsuc 4381 fsum2dlemstep 11335 fsumiun 11378 fprod2dlemstep 11523 |
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