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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 11213 | . 2 ⊢ 0 ∈ ℂ | |
2 | 1 | subidi 11538 | 1 ⊢ (0 − 0) = 0 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1540 (class class class)co 7412 0cc0 11116 − cmin 11451 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-10 2136 ax-11 2153 ax-12 2170 ax-ext 2702 ax-sep 5299 ax-nul 5306 ax-pow 5363 ax-pr 5427 ax-un 7729 ax-resscn 11173 ax-1cn 11174 ax-icn 11175 ax-addcl 11176 ax-addrcl 11177 ax-mulcl 11178 ax-mulrcl 11179 ax-mulcom 11180 ax-addass 11181 ax-mulass 11182 ax-distr 11183 ax-i2m1 11184 ax-1ne0 11185 ax-1rid 11186 ax-rnegex 11187 ax-rrecex 11188 ax-cnre 11189 ax-pre-lttri 11190 ax-pre-lttrn 11191 ax-pre-ltadd 11192 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-3or 1087 df-3an 1088 df-tru 1543 df-fal 1553 df-ex 1781 df-nf 1785 df-sb 2067 df-mo 2533 df-eu 2562 df-clab 2709 df-cleq 2723 df-clel 2809 df-nfc 2884 df-ne 2940 df-nel 3046 df-ral 3061 df-rex 3070 df-reu 3376 df-rab 3432 df-v 3475 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 6495 df-fun 6545 df-fn 6546 df-f 6547 df-f1 6548 df-fo 6549 df-f1o 6550 df-fv 6551 df-riota 7368 df-ov 7415 df-oprab 7416 df-mpo 7417 df-er 8709 df-en 8946 df-dom 8947 df-sdom 8948 df-pnf 11257 df-mnf 11258 df-ltxr 11260 df-sub 11453 |
This theorem is referenced by: discr 14210 revs1 14722 fsumparts 15759 binom 15783 arisum2 15814 0fallfac 15988 binomfallfac 15992 fsumcube 16011 phiprmpw 16716 prmreclem4 16859 srgbinom 20132 mhpmulcl 22002 rrxdstprj1 25258 ovolicc1 25366 itgrevallem1 25645 coeeulem 26077 plydiveu 26151 pilem2 26305 dcubic 26693 harmonicbnd3 26855 lgamgulmlem2 26877 logexprlim 27073 bposlem1 27132 bposlem2 27133 rplogsumlem2 27333 pntrsumo1 27413 pntrlog2bndlem4 27428 pntrlog2bndlem5 27429 pntleml 27459 axlowdimlem6 28640 0cnfn 31668 lnopeq0i 31695 ballotlemfval0 33960 ballotlem4 33963 ballotlemi1 33967 sgnneg 34005 fwddifn0 35608 mblfinlem2 36993 itg2addnclem 37006 itg2addnclem3 37008 lcmineqlem10 41373 acongeq 42188 mpaaeu 42358 dvnmul 45121 itgsinexplem1 45132 |
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