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Mirrors > Home > ILE Home > Th. List > djuf1olem | Unicode version |
Description: Lemma for djulf1o 6911 and djurf1o 6912. (Contributed by BJ and Jim Kingdon, 4-Jul-2022.) |
Ref | Expression |
---|---|
djuf1olem.1 | |
djuf1olem.2 |
Ref | Expression |
---|---|
djuf1olem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | djuf1olem.2 | . . 3 | |
2 | djuf1olem.1 | . . . . . 6 | |
3 | 2 | snid 3526 | . . . . 5 |
4 | opelxpi 4541 | . . . . 5 | |
5 | 3, 4 | mpan 420 | . . . 4 |
6 | 5 | adantl 275 | . . 3 |
7 | xp2nd 6032 | . . . 4 | |
8 | 7 | adantl 275 | . . 3 |
9 | 1st2nd2 6041 | . . . . . . . 8 | |
10 | xp1st 6031 | . . . . . . . . . 10 | |
11 | elsni 3515 | . . . . . . . . . 10 | |
12 | 10, 11 | syl 14 | . . . . . . . . 9 |
13 | 12 | opeq1d 3681 | . . . . . . . 8 |
14 | 9, 13 | eqtrd 2150 | . . . . . . 7 |
15 | 14 | eqeq2d 2129 | . . . . . 6 |
16 | eqcom 2119 | . . . . . 6 | |
17 | eqid 2117 | . . . . . . 7 | |
18 | vex 2663 | . . . . . . . 8 | |
19 | 2, 18 | opth 4129 | . . . . . . 7 |
20 | 17, 19 | mpbiran 909 | . . . . . 6 |
21 | 15, 16, 20 | 3bitr3g 221 | . . . . 5 |
22 | 21 | bicomd 140 | . . . 4 |
23 | 22 | ad2antll 482 | . . 3 |
24 | 1, 6, 8, 23 | f1o2d 5943 | . 2 |
25 | 24 | mptru 1325 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1316 wtru 1317 wcel 1465 cvv 2660 csn 3497 cop 3500 cmpt 3959 cxp 4507 wf1o 5092 cfv 5093 c1st 6004 c2nd 6005 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-un 4325 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-sbc 2883 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-mpt 3961 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-iota 5058 df-fun 5095 df-fn 5096 df-f 5097 df-f1 5098 df-fo 5099 df-f1o 5100 df-fv 5101 df-1st 6006 df-2nd 6007 |
This theorem is referenced by: djuf1olemr 6907 djulf1o 6911 djurf1o 6912 |
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