Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > iunxun | Unicode version |
Description: Separate a union in the index of an indexed union. (Contributed by NM, 26-Mar-2004.) (Proof shortened by Mario Carneiro, 17-Nov-2016.) |
Ref | Expression |
---|---|
iunxun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexun 3152 | . . . 4 | |
2 | eliun 3682 | . . . . 5 | |
3 | eliun 3682 | . . . . 5 | |
4 | 2, 3 | orbi12i 713 | . . . 4 |
5 | 1, 4 | bitr4i 185 | . . 3 |
6 | eliun 3682 | . . 3 | |
7 | elun 3113 | . . 3 | |
8 | 5, 6, 7 | 3bitr4i 210 | . 2 |
9 | 8 | eqriv 2078 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 661 wceq 1284 wcel 1433 wrex 2349 cun 2971 ciun 3678 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-iun 3680 |
This theorem is referenced by: iunsuc 4175 rdgisuc1 5994 oasuc 6067 omsuc 6074 |
Copyright terms: Public domain | W3C validator |