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Mirrors > Home > ILE Home > Th. List > ex-exp | Unicode version |
Description: Example for df-exp 10261. (Contributed by AV, 4-Sep-2021.) |
Ref | Expression |
---|---|
ex-exp | ; |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-5 8750 | . . . 4 | |
2 | 1 | oveq1i 5752 | . . 3 |
3 | 4cn 8766 | . . . . 5 | |
4 | binom21 10372 | . . . . 5 | |
5 | 3, 4 | ax-mp 5 | . . . 4 |
6 | 2nn0 8962 | . . . . 5 | |
7 | 4nn0 8964 | . . . . 5 | |
8 | 4p1e5 8824 | . . . . 5 | |
9 | sq4e2t8 10358 | . . . . . . . 8 | |
10 | 8cn 8774 | . . . . . . . . 9 | |
11 | 2cn 8759 | . . . . . . . . 9 | |
12 | 8t2e16 9264 | . . . . . . . . 9 ; | |
13 | 10, 11, 12 | mulcomli 7741 | . . . . . . . 8 ; |
14 | 9, 13 | eqtri 2138 | . . . . . . 7 ; |
15 | 4t2e8 8846 | . . . . . . . 8 | |
16 | 3, 11, 15 | mulcomli 7741 | . . . . . . 7 |
17 | 14, 16 | oveq12i 5754 | . . . . . 6 ; |
18 | 1nn0 8961 | . . . . . . 7 | |
19 | 6nn0 8966 | . . . . . . 7 | |
20 | 8nn0 8968 | . . . . . . 7 | |
21 | eqid 2117 | . . . . . . 7 ; ; | |
22 | 1p1e2 8805 | . . . . . . 7 | |
23 | 6cn 8770 | . . . . . . . 8 | |
24 | 8p6e14 9233 | . . . . . . . 8 ; | |
25 | 10, 23, 24 | addcomli 7875 | . . . . . . 7 ; |
26 | 18, 19, 20, 21, 22, 7, 25 | decaddci 9210 | . . . . . 6 ; ; |
27 | 17, 26 | eqtri 2138 | . . . . 5 ; |
28 | 6, 7, 8, 27 | decsuc 9180 | . . . 4 ; |
29 | 5, 28 | eqtri 2138 | . . 3 ; |
30 | 2, 29 | eqtri 2138 | . 2 ; |
31 | 3cn 8763 | . . . . 5 | |
32 | 31 | negcli 7998 | . . . 4 |
33 | 3ap0 8784 | . . . . 5 # | |
34 | negap0 8360 | . . . . . 6 # # | |
35 | 31, 34 | ax-mp 5 | . . . . 5 # # |
36 | 33, 35 | mpbi 144 | . . . 4 # |
37 | expnegap0 10269 | . . . 4 # | |
38 | 32, 36, 6, 37 | mp3an 1300 | . . 3 |
39 | sqneg 10320 | . . . . . 6 | |
40 | 31, 39 | ax-mp 5 | . . . . 5 |
41 | sq3 10357 | . . . . 5 | |
42 | 40, 41 | eqtri 2138 | . . . 4 |
43 | 42 | oveq2i 5753 | . . 3 |
44 | 38, 43 | eqtri 2138 | . 2 |
45 | 30, 44 | pm3.2i 270 | 1 ; |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1316 wcel 1465 class class class wbr 3899 (class class class)co 5742 cc 7586 cc0 7588 c1 7589 caddc 7591 cmul 7593 cneg 7902 # cap 8311 cdiv 8400 c2 8739 c3 8740 c4 8741 c5 8742 c6 8743 c8 8745 c9 8746 cn0 8945 ;cdc 9150 cexp 10260 |
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-coll 4013 ax-sep 4016 ax-nul 4024 ax-pow 4068 ax-pr 4101 ax-un 4325 ax-setind 4422 ax-iinf 4472 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-mulrcl 7687 ax-addcom 7688 ax-mulcom 7689 ax-addass 7690 ax-mulass 7691 ax-distr 7692 ax-i2m1 7693 ax-0lt1 7694 ax-1rid 7695 ax-0id 7696 ax-rnegex 7697 ax-precex 7698 ax-cnre 7699 ax-pre-ltirr 7700 ax-pre-ltwlin 7701 ax-pre-lttrn 7702 ax-pre-apti 7703 ax-pre-ltadd 7704 ax-pre-mulgt0 7705 ax-pre-mulext 7706 |
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-rmo 2401 df-rab 2402 df-v 2662 df-sbc 2883 df-csb 2976 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-if 3445 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-int 3742 df-iun 3785 df-br 3900 df-opab 3960 df-mpt 3961 df-tr 3997 df-id 4185 df-po 4188 df-iso 4189 df-iord 4258 df-on 4260 df-ilim 4261 df-suc 4263 df-iom 4475 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 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-riota 5698 df-ov 5745 df-oprab 5746 df-mpo 5747 df-1st 6006 df-2nd 6007 df-recs 6170 df-frec 6256 df-pnf 7770 df-mnf 7771 df-xr 7772 df-ltxr 7773 df-le 7774 df-sub 7903 df-neg 7904 df-reap 8305 df-ap 8312 df-div 8401 df-inn 8689 df-2 8747 df-3 8748 df-4 8749 df-5 8750 df-6 8751 df-7 8752 df-8 8753 df-9 8754 df-n0 8946 df-z 9023 df-dec 9151 df-uz 9295 df-seqfrec 10187 df-exp 10261 |
This theorem is referenced by: (None) |
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