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Mirrors > Home > MPE Home > Th. List > 0m0e0 | Structured version Visualization version GIF version |
Description: 0 minus 0 equals 0 (common case). (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
0m0e0 | ⊢ (0 − 0) = 0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0cn 9911 | . 2 ⊢ 0 ∈ ℂ | |
2 | 1 | subidi 10231 | 1 ⊢ (0 − 0) = 0 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 (class class class)co 6549 0cc0 9815 − cmin 10145 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-8 1979 ax-9 1986 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-sep 4709 ax-nul 4717 ax-pow 4769 ax-pr 4833 ax-un 6847 ax-resscn 9872 ax-1cn 9873 ax-icn 9874 ax-addcl 9875 ax-addrcl 9876 ax-mulcl 9877 ax-mulrcl 9878 ax-mulcom 9879 ax-addass 9880 ax-mulass 9881 ax-distr 9882 ax-i2m1 9883 ax-1ne0 9884 ax-1rid 9885 ax-rnegex 9886 ax-rrecex 9887 ax-cnre 9888 ax-pre-lttri 9889 ax-pre-lttrn 9890 ax-pre-ltadd 9891 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3or 1032 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-eu 2462 df-mo 2463 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ne 2782 df-nel 2783 df-ral 2901 df-rex 2902 df-reu 2903 df-rab 2905 df-v 3175 df-sbc 3403 df-csb 3500 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-if 4037 df-pw 4110 df-sn 4126 df-pr 4128 df-op 4132 df-uni 4373 df-br 4584 df-opab 4644 df-mpt 4645 df-id 4953 df-po 4959 df-so 4960 df-xp 5044 df-rel 5045 df-cnv 5046 df-co 5047 df-dm 5048 df-rn 5049 df-res 5050 df-ima 5051 df-iota 5768 df-fun 5806 df-fn 5807 df-f 5808 df-f1 5809 df-fo 5810 df-f1o 5811 df-fv 5812 df-riota 6511 df-ov 6552 df-oprab 6553 df-mpt2 6554 df-er 7629 df-en 7842 df-dom 7843 df-sdom 7844 df-pnf 9955 df-mnf 9956 df-ltxr 9958 df-sub 10147 |
This theorem is referenced by: discr 12863 swrdccat3a 13345 revs1 13365 fsumparts 14379 binom 14401 arisum2 14432 0fallfac 14607 binomfallfac 14611 fsumcube 14630 phiprmpw 15319 prmreclem4 15461 srgbinom 18368 rrxdstprj1 23000 ovolicc1 23091 itgrevallem1 23367 coeeulem 23784 plydiveu 23857 pilem2 24010 dcubic 24373 harmonicbnd3 24534 lgamgulmlem2 24556 logexprlim 24750 bposlem1 24809 bposlem2 24810 rplogsumlem2 24974 pntrsumo1 25054 pntrlog2bndlem4 25069 pntrlog2bndlem5 25070 pntleml 25100 axlowdimlem6 25627 0cnfn 28223 lnopeq0i 28250 ballotlemfval0 29884 ballotlem4 29887 ballotlemi1 29891 sgnneg 29929 fwddifn0 31441 mblfinlem2 32617 itg2addnclem 32631 itg2addnclem3 32633 acongeq 36568 mpaaeu 36739 dvnmul 38833 itgsinexplem1 38845 |
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