Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > resundir | Structured version Visualization version Unicode version |
Description: Distributive law for restriction over union. (Contributed by NM, 23-Sep-2004.) |
Ref | Expression |
---|---|
resundir |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | indir 3875 | . 2 | |
2 | df-res 5126 | . 2 | |
3 | df-res 5126 | . . 3 | |
4 | df-res 5126 | . . 3 | |
5 | 3, 4 | uneq12i 3765 | . 2 |
6 | 1, 2, 5 | 3eqtr4i 2654 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 cvv 3200 cun 3572 cin 3573 cxp 5112 cres 5116 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-un 3579 df-in 3581 df-res 5126 |
This theorem is referenced by: imaundir 5546 fresaunres2 6076 fvunsn 6445 fvsnun1 6448 fvsnun2 6449 fsnunfv 6453 fsnunres 6454 wfrlem14 7428 domss2 8119 axdc3lem4 9275 fseq1p1m1 12414 hashgval 13120 hashinf 13122 setsres 15901 setscom 15903 setsid 15914 pwssplit1 19059 ex-res 27298 funresdm1 29416 padct 29497 eulerpartlemt 30433 nosupbnd2lem1 31861 noetalem2 31864 noetalem3 31865 poimirlem3 33412 mapfzcons1 37280 diophrw 37322 eldioph2lem1 37323 eldioph2lem2 37324 diophin 37336 pwssplit4 37659 |
Copyright terms: Public domain | W3C validator |