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Mirrors > Home > ILE Home > Th. List > dfco2 | Unicode version |
Description: Alternate definition of a class composition, using only one bound variable. (Contributed by NM, 19-Dec-2008.) |
Ref | Expression |
---|---|
dfco2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relco 5007 | . 2 | |
2 | reliun 4630 | . . 3 | |
3 | relxp 4618 | . . . 4 | |
4 | 3 | a1i 9 | . . 3 |
5 | 2, 4 | mprgbir 2467 | . 2 |
6 | vex 2663 | . . . 4 | |
7 | vex 2663 | . . . 4 | |
8 | opelco2g 4677 | . . . 4 | |
9 | 6, 7, 8 | mp2an 422 | . . 3 |
10 | eliun 3787 | . . . 4 | |
11 | rexv 2678 | . . . 4 | |
12 | opelxp 4539 | . . . . . 6 | |
13 | vex 2663 | . . . . . . . . 9 | |
14 | 13, 6 | elimasn 4876 | . . . . . . . 8 |
15 | 13, 6 | opelcnv 4691 | . . . . . . . 8 |
16 | 14, 15 | bitri 183 | . . . . . . 7 |
17 | 13, 7 | elimasn 4876 | . . . . . . 7 |
18 | 16, 17 | anbi12i 455 | . . . . . 6 |
19 | 12, 18 | bitri 183 | . . . . 5 |
20 | 19 | exbii 1569 | . . . 4 |
21 | 10, 11, 20 | 3bitrri 206 | . . 3 |
22 | 9, 21 | bitri 183 | . 2 |
23 | 1, 5, 22 | eqrelriiv 4603 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1316 wex 1453 wcel 1465 wrex 2394 cvv 2660 csn 3497 cop 3500 ciun 3783 cxp 4507 ccnv 4508 cima 4512 ccom 4513 wrel 4514 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-sbc 2883 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-iun 3785 df-br 3900 df-opab 3960 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 |
This theorem is referenced by: dfco2a 5009 |
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