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Mirrors > Home > ILE Home > Th. List > dfiunv2 | Unicode version |
Description: Define double indexed union. (Contributed by FL, 6-Nov-2013.) |
Ref | Expression |
---|---|
dfiunv2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-iun 3862 | . . . 4 | |
2 | 1 | a1i 9 | . . 3 |
3 | 2 | iuneq2i 3878 | . 2 |
4 | df-iun 3862 | . 2 | |
5 | vex 2724 | . . . . 5 | |
6 | eleq1 2227 | . . . . . 6 | |
7 | 6 | rexbidv 2465 | . . . . 5 |
8 | 5, 7 | elab 2865 | . . . 4 |
9 | 8 | rexbii 2471 | . . 3 |
10 | 9 | abbii 2280 | . 2 |
11 | 3, 4, 10 | 3eqtri 2189 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 wcel 2135 cab 2150 wrex 2443 ciun 3860 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-in 3117 df-ss 3124 df-iun 3862 |
This theorem is referenced by: (None) |
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