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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 5867 | . 2 | |
2 | anass 398 | . . . 4 | |
3 | an4 575 | . . . . . 6 | |
4 | ssel 3091 | . . . . . . . . 9 | |
5 | 4 | pm4.71d 390 | . . . . . . . 8 |
6 | 5 | bicomd 140 | . . . . . . 7 |
7 | ssel 3091 | . . . . . . . . 9 | |
8 | 7 | pm4.71d 390 | . . . . . . . 8 |
9 | 8 | bicomd 140 | . . . . . . 7 |
10 | 6, 9 | bi2anan9 595 | . . . . . 6 |
11 | 3, 10 | syl5bb 191 | . . . . 5 |
12 | 11 | anbi1d 460 | . . . 4 |
13 | 2, 12 | syl5bbr 193 | . . 3 |
14 | 13 | oprabbidv 5825 | . 2 |
15 | 1, 14 | syl5eq 2184 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 wss 3071 cxp 4537 cres 4541 coprab 5775 |
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-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-opab 3990 df-xp 4545 df-rel 4546 df-res 4551 df-oprab 5778 |
This theorem is referenced by: resmpo 5869 |
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