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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 8979. (Contributed by David A. Wheeler, 4-Jan-2017.) |
Ref | Expression |
---|---|
2m1e1 | ⊢ (2 − 1) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2cn 8905 | . 2 ⊢ 2 ∈ ℂ | |
2 | ax-1cn 7826 | . 2 ⊢ 1 ∈ ℂ | |
3 | 1p1e2 8951 | . 2 ⊢ (1 + 1) = 2 | |
4 | 1, 2, 2, 3 | subaddrii 8165 | 1 ⊢ (2 − 1) = 1 |
Colors of variables: wff set class |
Syntax hints: = wceq 1335 (class class class)co 5825 1c1 7734 − cmin 8047 2c2 8885 |
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 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 ax-setind 4497 ax-resscn 7825 ax-1cn 7826 ax-1re 7827 ax-icn 7828 ax-addcl 7829 ax-addrcl 7830 ax-mulcl 7831 ax-addcom 7833 ax-addass 7835 ax-distr 7837 ax-i2m1 7838 ax-0id 7841 ax-rnegex 7842 ax-cnre 7844 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-ral 2440 df-rex 2441 df-reu 2442 df-rab 2444 df-v 2714 df-sbc 2938 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3774 df-br 3967 df-opab 4027 df-id 4254 df-xp 4593 df-rel 4594 df-cnv 4595 df-co 4596 df-dm 4597 df-iota 5136 df-fun 5173 df-fv 5179 df-riota 5781 df-ov 5828 df-oprab 5829 df-mpo 5830 df-sub 8049 df-2 8893 |
This theorem is referenced by: 1e2m1 8953 1mhlfehlf 9052 addltmul 9070 xp1d2m1eqxm1d2 9086 nn0lt2 9246 nn0le2is012 9247 zeo 9270 fzo0to2pr 10121 bcn2 10642 maxabslemlub 11111 geo2sum2 11416 ege2le3 11572 cos2tsin 11652 cos12dec 11668 odd2np1 11768 oddp1even 11771 mod2eq1n2dvds 11774 oddge22np1 11776 prmdiv 12114 sin0pilem1 13144 cos2pi 13167 cosq34lt1 13213 ex-fl 13343 |
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