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Mirrors > Home > MPE Home > Th. List > 0m0e0 | Structured version Visualization version GIF version |
Description: 0 minus 0 equals 0. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
0m0e0 | ⊢ (0 − 0) = 0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0cn 10622 | . 2 ⊢ 0 ∈ ℂ | |
2 | 1 | subidi 10946 | 1 ⊢ (0 − 0) = 0 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1538 (class class class)co 7135 0cc0 10526 − cmin 10859 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 ax-sep 5167 ax-nul 5174 ax-pow 5231 ax-pr 5295 ax-un 7441 ax-resscn 10583 ax-1cn 10584 ax-icn 10585 ax-addcl 10586 ax-addrcl 10587 ax-mulcl 10588 ax-mulrcl 10589 ax-mulcom 10590 ax-addass 10591 ax-mulass 10592 ax-distr 10593 ax-i2m1 10594 ax-1ne0 10595 ax-1rid 10596 ax-rnegex 10597 ax-rrecex 10598 ax-cnre 10599 ax-pre-lttri 10600 ax-pre-lttrn 10601 ax-pre-ltadd 10602 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-3or 1085 df-3an 1086 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-mo 2598 df-eu 2629 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-ne 2988 df-nel 3092 df-ral 3111 df-rex 3112 df-reu 3113 df-rab 3115 df-v 3443 df-sbc 3721 df-csb 3829 df-dif 3884 df-un 3886 df-in 3888 df-ss 3898 df-nul 4244 df-if 4426 df-pw 4499 df-sn 4526 df-pr 4528 df-op 4532 df-uni 4801 df-br 5031 df-opab 5093 df-mpt 5111 df-id 5425 df-po 5438 df-so 5439 df-xp 5525 df-rel 5526 df-cnv 5527 df-co 5528 df-dm 5529 df-rn 5530 df-res 5531 df-ima 5532 df-iota 6283 df-fun 6326 df-fn 6327 df-f 6328 df-f1 6329 df-fo 6330 df-f1o 6331 df-fv 6332 df-riota 7093 df-ov 7138 df-oprab 7139 df-mpo 7140 df-er 8272 df-en 8493 df-dom 8494 df-sdom 8495 df-pnf 10666 df-mnf 10667 df-ltxr 10669 df-sub 10861 |
This theorem is referenced by: discr 13597 revs1 14118 fsumparts 15153 binom 15177 arisum2 15208 0fallfac 15383 binomfallfac 15387 fsumcube 15406 phiprmpw 16103 prmreclem4 16245 srgbinom 19288 rrxdstprj1 24013 ovolicc1 24120 itgrevallem1 24398 coeeulem 24821 plydiveu 24894 pilem2 25047 dcubic 25432 harmonicbnd3 25593 lgamgulmlem2 25615 logexprlim 25809 bposlem1 25868 bposlem2 25869 rplogsumlem2 26069 pntrsumo1 26149 pntrlog2bndlem4 26164 pntrlog2bndlem5 26165 pntleml 26195 axlowdimlem6 26741 0cnfn 29763 lnopeq0i 29790 ballotlemfval0 31863 ballotlem4 31866 ballotlemi1 31870 sgnneg 31908 fwddifn0 33738 mblfinlem2 35095 itg2addnclem 35108 itg2addnclem3 35110 lcmineqlem10 39326 acongeq 39924 mpaaeu 40094 dvnmul 42585 itgsinexplem1 42596 |
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