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Mirrors > Home > ILE Home > Th. List > iunss | Unicode version |
Description: Subset theorem for an indexed union. (Contributed by NM, 13-Sep-2003.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
iunss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-iun 3851 | . . 3 | |
2 | 1 | sseq1i 3154 | . 2 |
3 | abss 3197 | . 2 | |
4 | dfss2 3117 | . . . 4 | |
5 | 4 | ralbii 2463 | . . 3 |
6 | ralcom4 2734 | . . 3 | |
7 | r19.23v 2566 | . . . 4 | |
8 | 7 | albii 1450 | . . 3 |
9 | 5, 6, 8 | 3bitrri 206 | . 2 |
10 | 2, 3, 9 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1333 wcel 2128 cab 2143 wral 2435 wrex 2436 wss 3102 ciun 3849 |
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-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-in 3108 df-ss 3115 df-iun 3851 |
This theorem is referenced by: iunss2 3894 djussxp 4731 fun11iun 5435 ennnfonelemf1 12158 tgidm 12485 |
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