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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 10186 | . 2 ⊢ 1 ∈ ℂ | |
2 | 1 | subid1i 10545 | 1 ⊢ (1 − 0) = 1 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1632 (class class class)co 6813 0cc0 10128 1c1 10129 − cmin 10458 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1871 ax-4 1886 ax-5 1988 ax-6 2054 ax-7 2090 ax-8 2141 ax-9 2148 ax-10 2168 ax-11 2183 ax-12 2196 ax-13 2391 ax-ext 2740 ax-sep 4933 ax-nul 4941 ax-pow 4992 ax-pr 5055 ax-un 7114 ax-resscn 10185 ax-1cn 10186 ax-icn 10187 ax-addcl 10188 ax-addrcl 10189 ax-mulcl 10190 ax-mulrcl 10191 ax-mulcom 10192 ax-addass 10193 ax-mulass 10194 ax-distr 10195 ax-i2m1 10196 ax-1ne0 10197 ax-1rid 10198 ax-rnegex 10199 ax-rrecex 10200 ax-cnre 10201 ax-pre-lttri 10202 ax-pre-lttrn 10203 ax-pre-ltadd 10204 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-3or 1073 df-3an 1074 df-tru 1635 df-ex 1854 df-nf 1859 df-sb 2047 df-eu 2611 df-mo 2612 df-clab 2747 df-cleq 2753 df-clel 2756 df-nfc 2891 df-ne 2933 df-nel 3036 df-ral 3055 df-rex 3056 df-reu 3057 df-rab 3059 df-v 3342 df-sbc 3577 df-csb 3675 df-dif 3718 df-un 3720 df-in 3722 df-ss 3729 df-nul 4059 df-if 4231 df-pw 4304 df-sn 4322 df-pr 4324 df-op 4328 df-uni 4589 df-br 4805 df-opab 4865 df-mpt 4882 df-id 5174 df-po 5187 df-so 5188 df-xp 5272 df-rel 5273 df-cnv 5274 df-co 5275 df-dm 5276 df-rn 5277 df-res 5278 df-ima 5279 df-iota 6012 df-fun 6051 df-fn 6052 df-f 6053 df-f1 6054 df-fo 6055 df-f1o 6056 df-fv 6057 df-riota 6774 df-ov 6816 df-oprab 6817 df-mpt2 6818 df-er 7911 df-en 8122 df-dom 8123 df-sdom 8124 df-pnf 10268 df-mnf 10269 df-ltxr 10271 df-sub 10460 |
This theorem is referenced by: xov1plusxeqvd 12511 fz1isolem 13437 trireciplem 14793 bpoly0 14980 bpoly1 14981 blcvx 22802 xrhmeo 22946 htpycom 22976 reparphti 22997 pcorevcl 23025 pcorevlem 23026 pi1xfrcnv 23057 vitalilem4 23579 vitalilem5 23580 dvef 23942 dvlipcn 23956 vieta1lem2 24265 dvtaylp 24323 taylthlem2 24327 tanregt0 24484 dvlog2lem 24597 logtayl 24605 atanlogaddlem 24839 leibpi 24868 scvxcvx 24911 emcllem7 24927 lgamgulmlem2 24955 rpvmasum 25414 brbtwn2 25984 axsegconlem1 25996 ax5seglem4 26011 axpaschlem 26019 axlowdimlem6 26026 axeuclid 26042 axcontlem2 26044 axcontlem4 26046 axcontlem8 26050 cvxpconn 31531 cvxsconn 31532 sinccvglem 31873 areacirclem4 33816 irrapxlem2 37889 pell1qr1 37937 jm2.18 38057 stoweidlem41 40761 stoweidlem45 40765 stirlinglem1 40794 difmodm1lt 42827 amgmwlem 43061 |
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