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Mirrors > Home > ILE Home > Th. List > Mathboxes > sumdc2 | Unicode version |
Description: Alternate proof of sumdc 11095, without disjoint variable condition on (longer because the statement is taylored to the proof sumdc 11095). (Contributed by BJ, 19-Feb-2022.) |
Ref | Expression |
---|---|
sumdc2.m | |
sumdc2.ss | |
sumdc2.dc | DECID |
sumdc2.n |
Ref | Expression |
---|---|
sumdc2 | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sumdc2.ss | . . 3 | |
2 | sumdc2.dc | . . . . 5 DECID | |
3 | eleq1 2180 | . . . . . . . 8 | |
4 | 3 | dcbid 808 | . . . . . . 7 DECID DECID |
5 | 4 | rspccv 2760 | . . . . . 6 DECID DECID |
6 | exmiddc 806 | . . . . . 6 DECID | |
7 | 5, 6 | syl6 33 | . . . . 5 DECID |
8 | 2, 7 | syl 14 | . . . 4 |
9 | 8 | decidr 12930 | . . 3 DECIDin |
10 | sumdc2.m | . . . 4 | |
11 | uzdcinzz 12932 | . . . 4 DECIDin | |
12 | 10, 11 | syl 14 | . . 3 DECIDin |
13 | 1, 9, 12 | decidin 12931 | . 2 DECIDin |
14 | sumdc2.n | . 2 | |
15 | df-dcin 12928 | . . 3 DECIDin DECID | |
16 | nfv 1493 | . . . . . 6 DECID | |
17 | 16 | rspct 2756 | . . . . 5 DECID DECID DECID DECID |
18 | eleq1 2180 | . . . . . 6 | |
19 | 18 | dcbid 808 | . . . . 5 DECID DECID |
20 | 17, 19 | mpg 1412 | . . . 4 DECID DECID |
21 | 20 | com12 30 | . . 3 DECID DECID |
22 | 15, 21 | sylbi 120 | . 2 DECIDin DECID |
23 | 13, 14, 22 | sylc 62 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wo 682 DECID wdc 804 wceq 1316 wcel 1465 wral 2393 wss 3041 cfv 5093 cz 9022 cuz 9294 DECIDin wdcin 12927 |
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-in1 588 ax-in2 589 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 ax-setind 4422 ax-cnex 7679 ax-resscn 7680 ax-1cn 7681 ax-1re 7682 ax-icn 7683 ax-addcl 7684 ax-addrcl 7685 ax-mulcl 7686 ax-addcom 7688 ax-addass 7690 ax-distr 7692 ax-i2m1 7693 ax-0lt1 7694 ax-0id 7696 ax-rnegex 7697 ax-cnre 7699 ax-pre-ltirr 7700 ax-pre-ltwlin 7701 ax-pre-lttrn 7702 ax-pre-ltadd 7704 |
This theorem depends on definitions: df-bi 116 df-dc 805 df-3or 948 df-3an 949 df-tru 1319 df-fal 1322 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-ne 2286 df-nel 2381 df-ral 2398 df-rex 2399 df-reu 2400 df-rab 2402 df-v 2662 df-sbc 2883 df-dif 3043 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-int 3742 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-iota 5058 df-fun 5095 df-fv 5101 df-riota 5698 df-ov 5745 df-oprab 5746 df-mpo 5747 df-pnf 7770 df-mnf 7771 df-xr 7772 df-ltxr 7773 df-le 7774 df-sub 7903 df-neg 7904 df-inn 8689 df-n0 8946 df-z 9023 df-uz 9295 df-dcin 12928 |
This theorem is referenced by: (None) |
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