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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 5917 | . 2 | |
2 | anass 399 | . . . 4 | |
3 | an4 576 | . . . . . 6 | |
4 | ssel 3122 | . . . . . . . . 9 | |
5 | 4 | pm4.71d 391 | . . . . . . . 8 |
6 | 5 | bicomd 140 | . . . . . . 7 |
7 | ssel 3122 | . . . . . . . . 9 | |
8 | 7 | pm4.71d 391 | . . . . . . . 8 |
9 | 8 | bicomd 140 | . . . . . . 7 |
10 | 6, 9 | bi2anan9 596 | . . . . . 6 |
11 | 3, 10 | syl5bb 191 | . . . . 5 |
12 | 11 | anbi1d 461 | . . . 4 |
13 | 2, 12 | bitr3id 193 | . . 3 |
14 | 13 | oprabbidv 5875 | . 2 |
15 | 1, 14 | syl5eq 2202 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wcel 2128 wss 3102 cxp 4584 cres 4588 coprab 5825 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-opab 4026 df-xp 4592 df-rel 4593 df-res 4598 df-oprab 5828 |
This theorem is referenced by: resmpo 5919 |
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