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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 5037 | . 2 | |
2 | reliun 4660 | . . 3 | |
3 | relxp 4648 | . . . 4 | |
4 | 3 | a1i 9 | . . 3 |
5 | 2, 4 | mprgbir 2490 | . 2 |
6 | vex 2689 | . . . 4 | |
7 | vex 2689 | . . . 4 | |
8 | opelco2g 4707 | . . . 4 | |
9 | 6, 7, 8 | mp2an 422 | . . 3 |
10 | eliun 3817 | . . . 4 | |
11 | rexv 2704 | . . . 4 | |
12 | opelxp 4569 | . . . . . 6 | |
13 | vex 2689 | . . . . . . . . 9 | |
14 | 13, 6 | elimasn 4906 | . . . . . . . 8 |
15 | 13, 6 | opelcnv 4721 | . . . . . . . 8 |
16 | 14, 15 | bitri 183 | . . . . . . 7 |
17 | 13, 7 | elimasn 4906 | . . . . . . 7 |
18 | 16, 17 | anbi12i 455 | . . . . . 6 |
19 | 12, 18 | bitri 183 | . . . . 5 |
20 | 19 | exbii 1584 | . . . 4 |
21 | 10, 11, 20 | 3bitrri 206 | . . 3 |
22 | 9, 21 | bitri 183 | . 2 |
23 | 1, 5, 22 | eqrelriiv 4633 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1331 wex 1468 wcel 1480 wrex 2417 cvv 2686 csn 3527 cop 3530 ciun 3813 cxp 4537 ccnv 4538 cima 4542 ccom 4543 wrel 4544 |
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-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-sbc 2910 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-iun 3815 df-br 3930 df-opab 3990 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 |
This theorem is referenced by: dfco2a 5039 |
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