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Mirrors > Home > ILE Home > Th. List > resundi | Unicode version |
Description: Distributive law for restriction over union. Theorem 31 of [Suppes] p. 65. (Contributed by NM, 30-Sep-2002.) |
Ref | Expression |
---|---|
resundi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpundir 4397 | . . . 4 | |
2 | 1 | ineq2i 3135 | . . 3 |
3 | indi 3184 | . . 3 | |
4 | 2, 3 | eqtri 2060 | . 2 |
5 | df-res 4357 | . 2 | |
6 | df-res 4357 | . . 3 | |
7 | df-res 4357 | . . 3 | |
8 | 6, 7 | uneq12i 3095 | . 2 |
9 | 4, 5, 8 | 3eqtr4i 2070 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1243 cvv 2557 cun 2915 cin 2916 cxp 4343 cres 4347 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-in 2924 df-opab 3819 df-xp 4351 df-res 4357 |
This theorem is referenced by: imaundi 4736 relresfld 4847 relcoi1 4849 resasplitss 5069 fseq1p1m1 8956 |
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