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Mirrors > Home > MPE Home > Th. List > 1m0e1 | Structured version Visualization version GIF version |
Description: 1 - 0 = 1. (Contributed by David A. Wheeler, 8-Dec-2018.) |
Ref | Expression |
---|---|
1m0e1 | ⊢ (1 − 0) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1cn 10332 | . 2 ⊢ 1 ∈ ℂ | |
2 | 1 | subid1i 10697 | 1 ⊢ (1 − 0) = 1 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1601 (class class class)co 6924 0cc0 10274 1c1 10275 − cmin 10608 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2055 ax-8 2109 ax-9 2116 ax-10 2135 ax-11 2150 ax-12 2163 ax-13 2334 ax-ext 2754 ax-sep 5019 ax-nul 5027 ax-pow 5079 ax-pr 5140 ax-un 7228 ax-resscn 10331 ax-1cn 10332 ax-icn 10333 ax-addcl 10334 ax-addrcl 10335 ax-mulcl 10336 ax-mulrcl 10337 ax-mulcom 10338 ax-addass 10339 ax-mulass 10340 ax-distr 10341 ax-i2m1 10342 ax-1ne0 10343 ax-1rid 10344 ax-rnegex 10345 ax-rrecex 10346 ax-cnre 10347 ax-pre-lttri 10348 ax-pre-lttrn 10349 ax-pre-ltadd 10350 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 837 df-3or 1072 df-3an 1073 df-tru 1605 df-ex 1824 df-nf 1828 df-sb 2012 df-mo 2551 df-eu 2587 df-clab 2764 df-cleq 2770 df-clel 2774 df-nfc 2921 df-ne 2970 df-nel 3076 df-ral 3095 df-rex 3096 df-reu 3097 df-rab 3099 df-v 3400 df-sbc 3653 df-csb 3752 df-dif 3795 df-un 3797 df-in 3799 df-ss 3806 df-nul 4142 df-if 4308 df-pw 4381 df-sn 4399 df-pr 4401 df-op 4405 df-uni 4674 df-br 4889 df-opab 4951 df-mpt 4968 df-id 5263 df-po 5276 df-so 5277 df-xp 5363 df-rel 5364 df-cnv 5365 df-co 5366 df-dm 5367 df-rn 5368 df-res 5369 df-ima 5370 df-iota 6101 df-fun 6139 df-fn 6140 df-f 6141 df-f1 6142 df-fo 6143 df-f1o 6144 df-fv 6145 df-riota 6885 df-ov 6927 df-oprab 6928 df-mpt2 6929 df-er 8028 df-en 8244 df-dom 8245 df-sdom 8246 df-pnf 10415 df-mnf 10416 df-ltxr 10418 df-sub 10610 |
This theorem is referenced by: xov1plusxeqvd 12639 fz1isolem 13563 trireciplem 15002 bpoly0 15187 bpoly1 15188 blcvx 23013 xrhmeo 23157 htpycom 23187 reparphti 23208 pcorevcl 23236 pcorevlem 23237 pi1xfrcnv 23268 vitalilem4 23819 vitalilem5 23820 dvef 24184 dvlipcn 24198 vieta1lem2 24507 dvtaylp 24565 taylthlem2 24569 tanregt0 24727 dvlog2lem 24839 logtayl 24847 atanlogaddlem 25095 leibpi 25125 scvxcvx 25168 emcllem7 25184 lgamgulmlem2 25212 rpvmasum 25671 brbtwn2 26258 axsegconlem1 26270 ax5seglem4 26285 axpaschlem 26293 axlowdimlem6 26300 axeuclid 26316 axcontlem2 26318 axcontlem4 26320 axcontlem8 26324 elntg2 26338 cvxpconn 31827 cvxsconn 31828 sinccvglem 32167 areacirclem4 34133 irrapxlem2 38357 pell1qr1 38405 jm2.18 38524 stoweidlem41 41195 stoweidlem45 41199 stirlinglem1 41228 difmodm1lt 43342 line2 43498 line2x 43500 amgmwlem 43664 |
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