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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 4819 | . 2 | |
2 | reliun 4458 | . . 3 | |
3 | relxp 4447 | . . . 4 | |
4 | 3 | a1i 9 | . . 3 |
5 | 2, 4 | mprgbir 2379 | . 2 |
6 | vex 2560 | . . . 4 | |
7 | vex 2560 | . . . 4 | |
8 | opelco2g 4503 | . . . 4 | |
9 | 6, 7, 8 | mp2an 402 | . . 3 |
10 | eliun 3661 | . . . 4 | |
11 | rexv 2572 | . . . 4 | |
12 | opelxp 4374 | . . . . . 6 | |
13 | vex 2560 | . . . . . . . . 9 | |
14 | 13, 6 | elimasn 4692 | . . . . . . . 8 |
15 | 13, 6 | opelcnv 4517 | . . . . . . . 8 |
16 | 14, 15 | bitri 173 | . . . . . . 7 |
17 | 13, 7 | elimasn 4692 | . . . . . . 7 |
18 | 16, 17 | anbi12i 433 | . . . . . 6 |
19 | 12, 18 | bitri 173 | . . . . 5 |
20 | 19 | exbii 1496 | . . . 4 |
21 | 10, 11, 20 | 3bitrri 196 | . . 3 |
22 | 9, 21 | bitri 173 | . 2 |
23 | 1, 5, 22 | eqrelriiv 4434 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wb 98 wceq 1243 wex 1381 wcel 1393 wrex 2307 cvv 2557 csn 3375 cop 3378 ciun 3657 cxp 4343 ccnv 4344 cima 4348 ccom 4349 wrel 4350 |
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-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-sbc 2765 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-iun 3659 df-br 3765 df-opab 3819 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-rn 4356 df-res 4357 df-ima 4358 |
This theorem is referenced by: dfco2a 4821 |
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