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Mirrors > Home > ILE Home > Th. List > resundir | Unicode version |
Description: Distributive law for restriction over union. (Contributed by NM, 23-Sep-2004.) |
Ref | Expression |
---|---|
resundir |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | indir 3325 | . 2 | |
2 | df-res 4551 | . 2 | |
3 | df-res 4551 | . . 3 | |
4 | df-res 4551 | . . 3 | |
5 | 3, 4 | uneq12i 3228 | . 2 |
6 | 1, 2, 5 | 3eqtr4i 2170 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 cvv 2686 cun 3069 cin 3070 cxp 4537 cres 4541 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-in 3077 df-res 4551 |
This theorem is referenced by: imaundir 4952 fvunsng 5614 fvsnun1 5617 fvsnun2 5618 fsnunfv 5621 fsnunres 5622 fseq1p1m1 9874 setsresg 11997 setscom 11999 setsslid 12009 |
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