Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > dfco2a | Unicode version |
Description: Generalization of dfco2 4820, 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 4820 | . 2 | |
2 | vex 2560 | . . . . . . . . . . . . . 14 | |
3 | vex 2560 | . . . . . . . . . . . . . . 15 | |
4 | 3 | eliniseg 4695 | . . . . . . . . . . . . . 14 |
5 | 2, 4 | ax-mp 7 | . . . . . . . . . . . . 13 |
6 | 3, 2 | brelrn 4567 | . . . . . . . . . . . . 13 |
7 | 5, 6 | sylbi 114 | . . . . . . . . . . . 12 |
8 | vex 2560 | . . . . . . . . . . . . . 14 | |
9 | 2, 8 | elimasn 4692 | . . . . . . . . . . . . 13 |
10 | 2, 8 | opeldm 4538 | . . . . . . . . . . . . 13 |
11 | 9, 10 | sylbi 114 | . . . . . . . . . . . 12 |
12 | 7, 11 | anim12ci 322 | . . . . . . . . . . 11 |
13 | 12 | adantl 262 | . . . . . . . . . 10 |
14 | 13 | exlimivv 1776 | . . . . . . . . 9 |
15 | elxp 4362 | . . . . . . . . 9 | |
16 | elin 3126 | . . . . . . . . 9 | |
17 | 14, 15, 16 | 3imtr4i 190 | . . . . . . . 8 |
18 | ssel 2939 | . . . . . . . 8 | |
19 | 17, 18 | syl5 28 | . . . . . . 7 |
20 | 19 | pm4.71rd 374 | . . . . . 6 |
21 | 20 | exbidv 1706 | . . . . 5 |
22 | rexv 2572 | . . . . 5 | |
23 | df-rex 2312 | . . . . 5 | |
24 | 21, 22, 23 | 3bitr4g 212 | . . . 4 |
25 | eliun 3661 | . . . 4 | |
26 | eliun 3661 | . . . 4 | |
27 | 24, 25, 26 | 3bitr4g 212 | . . 3 |
28 | 27 | eqrdv 2038 | . 2 |
29 | 1, 28 | syl5eq 2084 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wex 1381 wcel 1393 wrex 2307 cvv 2557 cin 2916 wss 2917 csn 3375 cop 3378 ciun 3657 class class class wbr 3764 cxp 4343 ccnv 4344 cdm 4345 crn 4346 cima 4348 ccom 4349 |
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: (None) |
Copyright terms: Public domain | W3C validator |