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Mirrors > Home > ILE Home > Th. List > resoprab2 | Unicode version |
Description: Restriction of an operator abstraction. (Contributed by Jeff Madsen, 2-Sep-2009.) |
Ref | Expression |
---|---|
resoprab2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resoprab 5597 | . 2 | |
2 | anass 381 | . . . 4 | |
3 | an4 520 | . . . . . 6 | |
4 | ssel 2939 | . . . . . . . . 9 | |
5 | 4 | pm4.71d 373 | . . . . . . . 8 |
6 | 5 | bicomd 129 | . . . . . . 7 |
7 | ssel 2939 | . . . . . . . . 9 | |
8 | 7 | pm4.71d 373 | . . . . . . . 8 |
9 | 8 | bicomd 129 | . . . . . . 7 |
10 | 6, 9 | bi2anan9 538 | . . . . . 6 |
11 | 3, 10 | syl5bb 181 | . . . . 5 |
12 | 11 | anbi1d 438 | . . . 4 |
13 | 2, 12 | syl5bbr 183 | . . 3 |
14 | 13 | oprabbidv 5559 | . 2 |
15 | 1, 14 | syl5eq 2084 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wceq 1243 wcel 1393 wss 2917 cxp 4343 cres 4347 coprab 5513 |
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 df-oprab 5516 |
This theorem is referenced by: resmpt2 5599 |
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