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Mirrors > Home > MPE Home > Th. List > 1div1e1 | Structured version Visualization version GIF version |
Description: 1 divided by 1 is 1. (Contributed by David A. Wheeler, 7-Dec-2018.) |
Ref | Expression |
---|---|
1div1e1 | ⊢ (1 / 1) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1cn 10673 | . 2 ⊢ 1 ∈ ℂ | |
2 | div1 11407 | . 2 ⊢ (1 ∈ ℂ → (1 / 1) = 1) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (1 / 1) = 1 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 ∈ wcel 2114 (class class class)co 7170 ℂcc 10613 1c1 10616 / cdiv 11375 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2162 ax-12 2179 ax-ext 2710 ax-sep 5167 ax-nul 5174 ax-pow 5232 ax-pr 5296 ax-un 7479 ax-resscn 10672 ax-1cn 10673 ax-icn 10674 ax-addcl 10675 ax-addrcl 10676 ax-mulcl 10677 ax-mulrcl 10678 ax-mulcom 10679 ax-addass 10680 ax-mulass 10681 ax-distr 10682 ax-i2m1 10683 ax-1ne0 10684 ax-1rid 10685 ax-rnegex 10686 ax-rrecex 10687 ax-cnre 10688 ax-pre-lttri 10689 ax-pre-lttrn 10690 ax-pre-ltadd 10691 ax-pre-mulgt0 10692 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 847 df-3or 1089 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1787 df-nf 1791 df-sb 2075 df-mo 2540 df-eu 2570 df-clab 2717 df-cleq 2730 df-clel 2811 df-nfc 2881 df-ne 2935 df-nel 3039 df-ral 3058 df-rex 3059 df-reu 3060 df-rmo 3061 df-rab 3062 df-v 3400 df-sbc 3681 df-csb 3791 df-dif 3846 df-un 3848 df-in 3850 df-ss 3860 df-nul 4212 df-if 4415 df-pw 4490 df-sn 4517 df-pr 4519 df-op 4523 df-uni 4797 df-br 5031 df-opab 5093 df-mpt 5111 df-id 5429 df-po 5442 df-so 5443 df-xp 5531 df-rel 5532 df-cnv 5533 df-co 5534 df-dm 5535 df-rn 5536 df-res 5537 df-ima 5538 df-iota 6297 df-fun 6341 df-fn 6342 df-f 6343 df-f1 6344 df-fo 6345 df-f1o 6346 df-fv 6347 df-riota 7127 df-ov 7173 df-oprab 7174 df-mpo 7175 df-er 8320 df-en 8556 df-dom 8557 df-sdom 8558 df-pnf 10755 df-mnf 10756 df-xr 10757 df-ltxr 10758 df-le 10759 df-sub 10950 df-neg 10951 df-div 11376 |
This theorem is referenced by: recdiv 11424 reclt1 11613 recgt1 11614 halflt1 11934 expneg 13529 m1expcl2 13543 1exp 13550 resqrex 14700 trireciplem 15310 fproddiv 15407 ef0lem 15524 eft0val 15557 m1expaddsub 18744 gzrngunit 20283 cnmsgnsubg 20393 psgninv 20398 vitali 24365 advlogexp 25398 logtayllem 25402 efrlim 25707 emcllem2 25734 emcllem7 25739 logexprlim 25961 dchrinvcl 25989 bclbnd 26016 lgseisenlem1 26111 lgseisenlem2 26112 lgsquadlem1 26116 dchrmusum2 26230 dchrvmasum2lem 26232 mulogsum 26268 pntrsumo1 26301 pnt2 26349 pnt 26350 qqh1 31505 faclimlem1 33280 faclim 33283 pellexlem2 40224 elpell1qr2 40266 bccn0 41499 binomcxplemradcnv 41508 mccl 42681 dvnprodlem3 43031 stoweidlem13 43096 stoweidlem42 43125 fourierdlem62 43251 iinhoiicclem 43753 sec0 45915 |
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