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Mirrors > Home > ILE Home > Th. List > ex-exp | Unicode version |
Description: Example for df-exp 10293. (Contributed by AV, 4-Sep-2021.) |
Ref | Expression |
---|---|
ex-exp | ; |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-5 8782 | . . . 4 | |
2 | 1 | oveq1i 5784 | . . 3 |
3 | 4cn 8798 | . . . . 5 | |
4 | binom21 10404 | . . . . 5 | |
5 | 3, 4 | ax-mp 5 | . . . 4 |
6 | 2nn0 8994 | . . . . 5 | |
7 | 4nn0 8996 | . . . . 5 | |
8 | 4p1e5 8856 | . . . . 5 | |
9 | sq4e2t8 10390 | . . . . . . . 8 | |
10 | 8cn 8806 | . . . . . . . . 9 | |
11 | 2cn 8791 | . . . . . . . . 9 | |
12 | 8t2e16 9296 | . . . . . . . . 9 ; | |
13 | 10, 11, 12 | mulcomli 7773 | . . . . . . . 8 ; |
14 | 9, 13 | eqtri 2160 | . . . . . . 7 ; |
15 | 4t2e8 8878 | . . . . . . . 8 | |
16 | 3, 11, 15 | mulcomli 7773 | . . . . . . 7 |
17 | 14, 16 | oveq12i 5786 | . . . . . 6 ; |
18 | 1nn0 8993 | . . . . . . 7 | |
19 | 6nn0 8998 | . . . . . . 7 | |
20 | 8nn0 9000 | . . . . . . 7 | |
21 | eqid 2139 | . . . . . . 7 ; ; | |
22 | 1p1e2 8837 | . . . . . . 7 | |
23 | 6cn 8802 | . . . . . . . 8 | |
24 | 8p6e14 9265 | . . . . . . . 8 ; | |
25 | 10, 23, 24 | addcomli 7907 | . . . . . . 7 ; |
26 | 18, 19, 20, 21, 22, 7, 25 | decaddci 9242 | . . . . . 6 ; ; |
27 | 17, 26 | eqtri 2160 | . . . . 5 ; |
28 | 6, 7, 8, 27 | decsuc 9212 | . . . 4 ; |
29 | 5, 28 | eqtri 2160 | . . 3 ; |
30 | 2, 29 | eqtri 2160 | . 2 ; |
31 | 3cn 8795 | . . . . 5 | |
32 | 31 | negcli 8030 | . . . 4 |
33 | 3ap0 8816 | . . . . 5 # | |
34 | negap0 8392 | . . . . . 6 # # | |
35 | 31, 34 | ax-mp 5 | . . . . 5 # # |
36 | 33, 35 | mpbi 144 | . . . 4 # |
37 | expnegap0 10301 | . . . 4 # | |
38 | 32, 36, 6, 37 | mp3an 1315 | . . 3 |
39 | sqneg 10352 | . . . . . 6 | |
40 | 31, 39 | ax-mp 5 | . . . . 5 |
41 | sq3 10389 | . . . . 5 | |
42 | 40, 41 | eqtri 2160 | . . . 4 |
43 | 42 | oveq2i 5785 | . . 3 |
44 | 38, 43 | eqtri 2160 | . 2 |
45 | 30, 44 | pm3.2i 270 | 1 ; |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1331 wcel 1480 class class class wbr 3929 (class class class)co 5774 cc 7618 cc0 7620 c1 7621 caddc 7623 cmul 7625 cneg 7934 # cap 8343 cdiv 8432 c2 8771 c3 8772 c4 8773 c5 8774 c6 8775 c8 8777 c9 8778 cn0 8977 ;cdc 9182 cexp 10292 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-coll 4043 ax-sep 4046 ax-nul 4054 ax-pow 4098 ax-pr 4131 ax-un 4355 ax-setind 4452 ax-iinf 4502 ax-cnex 7711 ax-resscn 7712 ax-1cn 7713 ax-1re 7714 ax-icn 7715 ax-addcl 7716 ax-addrcl 7717 ax-mulcl 7718 ax-mulrcl 7719 ax-addcom 7720 ax-mulcom 7721 ax-addass 7722 ax-mulass 7723 ax-distr 7724 ax-i2m1 7725 ax-0lt1 7726 ax-1rid 7727 ax-0id 7728 ax-rnegex 7729 ax-precex 7730 ax-cnre 7731 ax-pre-ltirr 7732 ax-pre-ltwlin 7733 ax-pre-lttrn 7734 ax-pre-apti 7735 ax-pre-ltadd 7736 ax-pre-mulgt0 7737 ax-pre-mulext 7738 |
This theorem depends on definitions: df-bi 116 df-dc 820 df-3or 963 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-nel 2404 df-ral 2421 df-rex 2422 df-reu 2423 df-rmo 2424 df-rab 2425 df-v 2688 df-sbc 2910 df-csb 3004 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-nul 3364 df-if 3475 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-int 3772 df-iun 3815 df-br 3930 df-opab 3990 df-mpt 3991 df-tr 4027 df-id 4215 df-po 4218 df-iso 4219 df-iord 4288 df-on 4290 df-ilim 4291 df-suc 4293 df-iom 4505 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-f1 5128 df-fo 5129 df-f1o 5130 df-fv 5131 df-riota 5730 df-ov 5777 df-oprab 5778 df-mpo 5779 df-1st 6038 df-2nd 6039 df-recs 6202 df-frec 6288 df-pnf 7802 df-mnf 7803 df-xr 7804 df-ltxr 7805 df-le 7806 df-sub 7935 df-neg 7936 df-reap 8337 df-ap 8344 df-div 8433 df-inn 8721 df-2 8779 df-3 8780 df-4 8781 df-5 8782 df-6 8783 df-7 8784 df-8 8785 df-9 8786 df-n0 8978 df-z 9055 df-dec 9183 df-uz 9327 df-seqfrec 10219 df-exp 10293 |
This theorem is referenced by: (None) |
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