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Mirrors > Home > ILE Home > Th. List > 2m1e1 | GIF version |
Description: 2 - 1 = 1. The result is on the right-hand-side to be consistent with similar proofs like 4p4e8 8833. (Contributed by David A. Wheeler, 4-Jan-2017.) |
Ref | Expression |
---|---|
2m1e1 | ⊢ (2 − 1) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2cn 8759 | . 2 ⊢ 2 ∈ ℂ | |
2 | ax-1cn 7681 | . 2 ⊢ 1 ∈ ℂ | |
3 | 1p1e2 8805 | . 2 ⊢ (1 + 1) = 2 | |
4 | 1, 2, 2, 3 | subaddrii 8019 | 1 ⊢ (2 − 1) = 1 |
Colors of variables: wff set class |
Syntax hints: = wceq 1316 (class class class)co 5742 1c1 7589 − cmin 7901 2c2 8739 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-setind 4422 ax-resscn 7680 ax-1cn 7681 ax-1re 7682 ax-icn 7683 ax-addcl 7684 ax-addrcl 7685 ax-mulcl 7686 ax-addcom 7688 ax-addass 7690 ax-distr 7692 ax-i2m1 7693 ax-0id 7696 ax-rnegex 7697 ax-cnre 7699 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-ral 2398 df-rex 2399 df-reu 2400 df-rab 2402 df-v 2662 df-sbc 2883 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-iota 5058 df-fun 5095 df-fv 5101 df-riota 5698 df-ov 5745 df-oprab 5746 df-mpo 5747 df-sub 7903 df-2 8747 |
This theorem is referenced by: 1e2m1 8807 1mhlfehlf 8906 addltmul 8924 xp1d2m1eqxm1d2 8940 nn0lt2 9100 nn0le2is012 9101 zeo 9124 fzo0to2pr 9963 bcn2 10478 maxabslemlub 10947 geo2sum2 11252 ege2le3 11304 cos2tsin 11385 cos12dec 11401 odd2np1 11497 oddp1even 11500 mod2eq1n2dvds 11503 oddge22np1 11505 sin0pilem1 12789 cos2pi 12812 cosq34lt1 12858 ex-fl 12864 |
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