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Mirrors > Home > ILE Home > Th. List > dfco2a | Unicode version |
Description: Generalization of dfco2 5038, where can have any value between and . (Contributed by NM, 21-Dec-2008.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
dfco2a |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfco2 5038 | . 2 | |
2 | vex 2689 | . . . . . . . . . . . . . 14 | |
3 | vex 2689 | . . . . . . . . . . . . . . 15 | |
4 | 3 | eliniseg 4909 | . . . . . . . . . . . . . 14 |
5 | 2, 4 | ax-mp 5 | . . . . . . . . . . . . 13 |
6 | 3, 2 | brelrn 4772 | . . . . . . . . . . . . 13 |
7 | 5, 6 | sylbi 120 | . . . . . . . . . . . 12 |
8 | vex 2689 | . . . . . . . . . . . . . 14 | |
9 | 2, 8 | elimasn 4906 | . . . . . . . . . . . . 13 |
10 | 2, 8 | opeldm 4742 | . . . . . . . . . . . . 13 |
11 | 9, 10 | sylbi 120 | . . . . . . . . . . . 12 |
12 | 7, 11 | anim12ci 337 | . . . . . . . . . . 11 |
13 | 12 | adantl 275 | . . . . . . . . . 10 |
14 | 13 | exlimivv 1868 | . . . . . . . . 9 |
15 | elxp 4556 | . . . . . . . . 9 | |
16 | elin 3259 | . . . . . . . . 9 | |
17 | 14, 15, 16 | 3imtr4i 200 | . . . . . . . 8 |
18 | ssel 3091 | . . . . . . . 8 | |
19 | 17, 18 | syl5 32 | . . . . . . 7 |
20 | 19 | pm4.71rd 391 | . . . . . 6 |
21 | 20 | exbidv 1797 | . . . . 5 |
22 | rexv 2704 | . . . . 5 | |
23 | df-rex 2422 | . . . . 5 | |
24 | 21, 22, 23 | 3bitr4g 222 | . . . 4 |
25 | eliun 3817 | . . . 4 | |
26 | eliun 3817 | . . . 4 | |
27 | 24, 25, 26 | 3bitr4g 222 | . . 3 |
28 | 27 | eqrdv 2137 | . 2 |
29 | 1, 28 | syl5eq 2184 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wex 1468 wcel 1480 wrex 2417 cvv 2686 cin 3070 wss 3071 csn 3527 cop 3530 ciun 3813 class class class wbr 3929 cxp 4537 ccnv 4538 cdm 4539 crn 4540 cima 4542 ccom 4543 |
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: (None) |
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