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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 11172 | . 2 ⊢ 1 ∈ ℂ | |
2 | 1 | subid1i 11537 | 1 ⊢ (1 − 0) = 1 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1540 (class class class)co 7412 0cc0 11114 1c1 11115 − cmin 11449 |
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 11171 ax-1cn 11172 ax-icn 11173 ax-addcl 11174 ax-addrcl 11175 ax-mulcl 11176 ax-mulrcl 11177 ax-mulcom 11178 ax-addass 11179 ax-mulass 11180 ax-distr 11181 ax-i2m1 11182 ax-1ne0 11183 ax-1rid 11184 ax-rnegex 11185 ax-rrecex 11186 ax-cnre 11187 ax-pre-lttri 11188 ax-pre-lttrn 11189 ax-pre-ltadd 11190 |
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 8707 df-en 8944 df-dom 8945 df-sdom 8946 df-pnf 11255 df-mnf 11256 df-ltxr 11258 df-sub 11451 |
This theorem is referenced by: xov1plusxeqvd 13480 fz1isolem 14427 trireciplem 15813 bpoly0 15999 bpoly1 16000 pzriprng1ALT 21266 blcvx 24535 xrhmeo 24692 htpycom 24723 reparphti 24744 reparphtiOLD 24745 pcorevcl 24773 pcorevlem 24774 pi1xfrcnv 24805 vitalilem4 25361 vitalilem5 25362 dvef 25733 dvlipcn 25747 vieta1lem2 26061 dvtaylp 26119 taylthlem2 26123 tanregt0 26285 dvlog2lem 26397 logtayl 26405 atanlogaddlem 26655 leibpi 26684 scvxcvx 26727 emcllem7 26743 lgamgulmlem2 26771 rpvmasum 27266 brbtwn2 28431 axsegconlem1 28443 ax5seglem4 28458 axpaschlem 28466 axlowdimlem6 28473 axeuclid 28489 axcontlem2 28491 axcontlem4 28493 axcontlem8 28497 elntg2 28511 cvxpconn 34532 cvxsconn 34533 sinccvglem 34956 areacirclem4 36883 lcmineqlem3 41203 lcmineqlem12 41212 irrapxlem2 41864 pell1qr1 41912 jm2.18 42030 stoweidlem41 45056 stoweidlem45 45060 stirlinglem1 45089 difmodm1lt 47296 line2 47526 line2x 47528 amgmwlem 47937 |
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