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Mirrors > Home > ILE Home > Th. List > resindi | Unicode version |
Description: Class restriction distributes over intersection. (Contributed by FL, 6-Oct-2008.) |
Ref | Expression |
---|---|
resindi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpindir 4472 | . . . 4 | |
2 | 1 | ineq2i 3135 | . . 3 |
3 | inindi 3154 | . . 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 | ineq12i 3136 | . 2 |
9 | 4, 5, 8 | 3eqtr4i 2070 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1243 cvv 2557 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-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-opab 3819 df-xp 4351 df-rel 4352 df-res 4357 |
This theorem is referenced by: (None) |
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