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Mirrors > Home > MPE Home > Th. List > 3m1e2 | Structured version Visualization version GIF version |
Description: 3 - 1 = 2. (Contributed by FL, 17-Oct-2010.) (Revised by NM, 10-Dec-2017.) (Proof shortened by AV, 6-Sep-2021.) |
Ref | Expression |
---|---|
3m1e2 | ⊢ (3 − 1) = 2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2cn 11091 | . 2 ⊢ 2 ∈ ℂ | |
2 | ax-1cn 9994 | . 2 ⊢ 1 ∈ ℂ | |
3 | df-3 11080 | . 2 ⊢ 3 = (2 + 1) | |
4 | 1, 2, 3 | mvrraddi 10298 | 1 ⊢ (3 − 1) = 2 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1483 (class class class)co 6650 1c1 9937 − cmin 10266 2c2 11070 3c3 11071 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 ax-resscn 9993 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-addrcl 9997 ax-mulcl 9998 ax-mulrcl 9999 ax-mulcom 10000 ax-addass 10001 ax-mulass 10002 ax-distr 10003 ax-i2m1 10004 ax-1ne0 10005 ax-1rid 10006 ax-rnegex 10007 ax-rrecex 10008 ax-cnre 10009 ax-pre-lttri 10010 ax-pre-lttrn 10011 ax-pre-ltadd 10012 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-nel 2898 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-po 5035 df-so 5036 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-riota 6611 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-er 7742 df-en 7956 df-dom 7957 df-sdom 7958 df-pnf 10076 df-mnf 10077 df-ltxr 10079 df-sub 10268 df-2 11079 df-3 11080 |
This theorem is referenced by: halfpm6th 11253 ige3m2fz 12365 fzo13pr 12552 fzo0to3tp 12554 fldiv4p1lem1div2 12636 lsws3 13650 bpoly3 14789 rpnnen2lem3 14945 rpnnen2lem11 14953 n2dvds3 15107 3prm 15406 prmo3 15745 1cubrlem 24568 1cubr 24569 quart1 24583 log2cnv 24671 log2ublem3 24675 2lgslem3b 25122 2lgslem3d 25124 axlowdimlem16 25837 2pthd 26836 wlk2v2e 27017 ex-bc 27309 fib4 30466 circlemethhgt 30721 itg2addnclem3 33463 lhe4.4ex1a 38528 wallispilem4 40285 fmtnoge3 41442 fmtnoprmfac2lem1 41478 nnsum3primesle9 41682 |
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