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Mirrors > Home > ILE Home > Th. List > resiun1 | Unicode version |
Description: Distribution of restriction over indexed union. (Contributed by Mario Carneiro, 29-May-2015.) |
Ref | Expression |
---|---|
resiun1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iunin2 3741 | . 2 | |
2 | df-res 4375 | . . . . 5 | |
3 | incom 3158 | . . . . 5 | |
4 | 2, 3 | eqtri 2101 | . . . 4 |
5 | 4 | a1i 9 | . . 3 |
6 | 5 | iuneq2i 3696 | . 2 |
7 | df-res 4375 | . . 3 | |
8 | incom 3158 | . . 3 | |
9 | 7, 8 | eqtri 2101 | . 2 |
10 | 1, 6, 9 | 3eqtr4ri 2112 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1284 wcel 1433 cvv 2601 cin 2972 ciun 3678 cxp 4361 cres 4365 |
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-in 2979 df-ss 2986 df-iun 3680 df-res 4375 |
This theorem is referenced by: (None) |
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