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Mirrors > Home > ILE Home > Th. List > dfoprab3s | Unicode version |
Description: A way to define an operation class abstraction without using existential quantifiers. (Contributed by NM, 18-Aug-2006.) (Revised by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
dfoprab3s |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfoprab2 5572 | . 2 | |
2 | nfsbc1v 2833 | . . . . 5 | |
3 | 2 | 19.41 1616 | . . . 4 |
4 | sbcopeq1a 5833 | . . . . . . . 8 | |
5 | 4 | pm5.32i 441 | . . . . . . 7 |
6 | 5 | exbii 1536 | . . . . . 6 |
7 | nfcv 2219 | . . . . . . . 8 | |
8 | nfsbc1v 2833 | . . . . . . . 8 | |
9 | 7, 8 | nfsbc 2835 | . . . . . . 7 |
10 | 9 | 19.41 1616 | . . . . . 6 |
11 | 6, 10 | bitr3i 184 | . . . . 5 |
12 | 11 | exbii 1536 | . . . 4 |
13 | elvv 4420 | . . . . 5 | |
14 | 13 | anbi1i 445 | . . . 4 |
15 | 3, 12, 14 | 3bitr4i 210 | . . 3 |
16 | 15 | opabbii 3845 | . 2 |
17 | 1, 16 | eqtri 2101 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 wceq 1284 wex 1421 wcel 1433 cvv 2601 wsbc 2815 cop 3401 copab 3838 cxp 4361 cfv 4922 coprab 5533 c1st 5785 c2nd 5786 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 ax-un 4188 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-sbc 2816 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-mpt 3841 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-iota 4887 df-fun 4924 df-fv 4930 df-oprab 5536 df-1st 5787 df-2nd 5788 |
This theorem is referenced by: dfoprab3 5837 |
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