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Mirrors > Home > ILE Home > Th. List > dfco2a | Unicode version |
Description: Generalization of dfco2 5097, 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 5097 | . 2 | |
2 | vex 2724 | . . . . . . . . . . . . . 14 | |
3 | vex 2724 | . . . . . . . . . . . . . . 15 | |
4 | 3 | eliniseg 4968 | . . . . . . . . . . . . . 14 |
5 | 2, 4 | ax-mp 5 | . . . . . . . . . . . . 13 |
6 | 3, 2 | brelrn 4831 | . . . . . . . . . . . . 13 |
7 | 5, 6 | sylbi 120 | . . . . . . . . . . . 12 |
8 | vex 2724 | . . . . . . . . . . . . . 14 | |
9 | 2, 8 | elimasn 4965 | . . . . . . . . . . . . 13 |
10 | 2, 8 | opeldm 4801 | . . . . . . . . . . . . 13 |
11 | 9, 10 | sylbi 120 | . . . . . . . . . . . 12 |
12 | 7, 11 | anim12ci 337 | . . . . . . . . . . 11 |
13 | 12 | adantl 275 | . . . . . . . . . 10 |
14 | 13 | exlimivv 1883 | . . . . . . . . 9 |
15 | elxp 4615 | . . . . . . . . 9 | |
16 | elin 3300 | . . . . . . . . 9 | |
17 | 14, 15, 16 | 3imtr4i 200 | . . . . . . . 8 |
18 | ssel 3131 | . . . . . . . 8 | |
19 | 17, 18 | syl5 32 | . . . . . . 7 |
20 | 19 | pm4.71rd 392 | . . . . . 6 |
21 | 20 | exbidv 1812 | . . . . 5 |
22 | rexv 2739 | . . . . 5 | |
23 | df-rex 2448 | . . . . 5 | |
24 | 21, 22, 23 | 3bitr4g 222 | . . . 4 |
25 | eliun 3864 | . . . 4 | |
26 | eliun 3864 | . . . 4 | |
27 | 24, 25, 26 | 3bitr4g 222 | . . 3 |
28 | 27 | eqrdv 2162 | . 2 |
29 | 1, 28 | syl5eq 2209 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1342 wex 1479 wcel 2135 wrex 2443 cvv 2721 cin 3110 wss 3111 csn 3570 cop 3573 ciun 3860 class class class wbr 3976 cxp 4596 ccnv 4597 cdm 4598 crn 4599 cima 4601 ccom 4602 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-sbc 2947 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-iun 3862 df-br 3977 df-opab 4038 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-rn 4609 df-res 4610 df-ima 4611 |
This theorem is referenced by: (None) |
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