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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 5083 | . 2 | |
2 | reliun 4706 | . . 3 | |
3 | relxp 4694 | . . . 4 | |
4 | 3 | a1i 9 | . . 3 |
5 | 2, 4 | mprgbir 2515 | . 2 |
6 | vex 2715 | . . . 4 | |
7 | vex 2715 | . . . 4 | |
8 | opelco2g 4753 | . . . 4 | |
9 | 6, 7, 8 | mp2an 423 | . . 3 |
10 | eliun 3853 | . . . 4 | |
11 | rexv 2730 | . . . 4 | |
12 | opelxp 4615 | . . . . . 6 | |
13 | vex 2715 | . . . . . . . . 9 | |
14 | 13, 6 | elimasn 4952 | . . . . . . . 8 |
15 | 13, 6 | opelcnv 4767 | . . . . . . . 8 |
16 | 14, 15 | bitri 183 | . . . . . . 7 |
17 | 13, 7 | elimasn 4952 | . . . . . . 7 |
18 | 16, 17 | anbi12i 456 | . . . . . 6 |
19 | 12, 18 | bitri 183 | . . . . 5 |
20 | 19 | exbii 1585 | . . . 4 |
21 | 10, 11, 20 | 3bitrri 206 | . . 3 |
22 | 9, 21 | bitri 183 | . 2 |
23 | 1, 5, 22 | eqrelriiv 4679 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1335 wex 1472 wcel 2128 wrex 2436 cvv 2712 csn 3560 cop 3563 ciun 3849 cxp 4583 ccnv 4584 cima 4588 ccom 4589 wrel 4590 |
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-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-iun 3851 df-br 3966 df-opab 4026 df-xp 4591 df-rel 4592 df-cnv 4593 df-co 4594 df-dm 4595 df-rn 4596 df-res 4597 df-ima 4598 |
This theorem is referenced by: dfco2a 5085 |
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