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Mirrors > Home > ILE Home > Th. List > iunopab | Unicode version |
Description: Move indexed union inside an ordered-pair abstraction. (Contributed by Stefan O'Rear, 20-Feb-2015.) |
Ref | Expression |
---|---|
iunopab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elopab 4241 | . . . . 5 | |
2 | 1 | rexbii 2477 | . . . 4 |
3 | rexcom4 2753 | . . . . 5 | |
4 | rexcom4 2753 | . . . . . . 7 | |
5 | r19.42v 2627 | . . . . . . . 8 | |
6 | 5 | exbii 1598 | . . . . . . 7 |
7 | 4, 6 | bitri 183 | . . . . . 6 |
8 | 7 | exbii 1598 | . . . . 5 |
9 | 3, 8 | bitri 183 | . . . 4 |
10 | 2, 9 | bitri 183 | . . 3 |
11 | 10 | abbii 2286 | . 2 |
12 | df-iun 3873 | . 2 | |
13 | df-opab 4049 | . 2 | |
14 | 11, 12, 13 | 3eqtr4i 2201 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1348 wex 1485 wcel 2141 cab 2156 wrex 2449 cop 3584 ciun 3871 copab 4047 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3566 df-sn 3587 df-pr 3588 df-op 3590 df-iun 3873 df-opab 4049 |
This theorem is referenced by: (None) |
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