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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 11165 | . 2 ⊢ 1 ∈ ℂ | |
2 | div1 11900 | . 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 2107 (class class class)co 7406 ℂcc 11105 1c1 11108 / cdiv 11868 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-sep 5299 ax-nul 5306 ax-pow 5363 ax-pr 5427 ax-un 7722 ax-resscn 11164 ax-1cn 11165 ax-icn 11166 ax-addcl 11167 ax-addrcl 11168 ax-mulcl 11169 ax-mulrcl 11170 ax-mulcom 11171 ax-addass 11172 ax-mulass 11173 ax-distr 11174 ax-i2m1 11175 ax-1ne0 11176 ax-1rid 11177 ax-rnegex 11178 ax-rrecex 11179 ax-cnre 11180 ax-pre-lttri 11181 ax-pre-lttrn 11182 ax-pre-ltadd 11183 ax-pre-mulgt0 11184 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3or 1089 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2942 df-nel 3048 df-ral 3063 df-rex 3072 df-rmo 3377 df-reu 3378 df-rab 3434 df-v 3477 df-sbc 3778 df-csb 3894 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-nul 4323 df-if 4529 df-pw 4604 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-br 5149 df-opab 5211 df-mpt 5232 df-id 5574 df-po 5588 df-so 5589 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-rn 5687 df-res 5688 df-ima 5689 df-iota 6493 df-fun 6543 df-fn 6544 df-f 6545 df-f1 6546 df-fo 6547 df-f1o 6548 df-fv 6549 df-riota 7362 df-ov 7409 df-oprab 7410 df-mpo 7411 df-er 8700 df-en 8937 df-dom 8938 df-sdom 8939 df-pnf 11247 df-mnf 11248 df-xr 11249 df-ltxr 11250 df-le 11251 df-sub 11443 df-neg 11444 df-div 11869 |
This theorem is referenced by: recdiv 11917 reclt1 12106 recgt1 12107 halflt1 12427 expneg 14032 m1expcl2 14048 1exp 14054 resqrex 15194 trireciplem 15805 fproddiv 15902 ef0lem 16019 eft0val 16052 m1expaddsub 19361 gzrngunit 21004 cnmsgnsubg 21122 psgninv 21127 vitali 25122 advlogexp 26155 logtayllem 26159 efrlim 26464 emcllem2 26491 emcllem7 26496 logexprlim 26718 dchrinvcl 26746 bclbnd 26773 lgseisenlem1 26868 lgseisenlem2 26869 lgsquadlem1 26873 dchrmusum2 26987 dchrvmasum2lem 26989 mulogsum 27025 pntrsumo1 27058 pnt2 27106 pnt 27107 qqh1 32954 faclimlem1 34702 faclim 34705 pellexlem2 41554 elpell1qr2 41596 bccn0 43088 binomcxplemradcnv 43097 mccl 44301 dvnprodlem3 44651 stoweidlem13 44716 stoweidlem42 44745 fourierdlem62 44871 iinhoiicclem 45376 sec0 47759 |
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