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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 8622. (Contributed by David A. Wheeler, 4-Jan-2017.) |
Ref | Expression |
---|---|
2m1e1 | ⊢ (2 − 1) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2cn 8554 | . 2 ⊢ 2 ∈ ℂ | |
2 | ax-1cn 7499 | . 2 ⊢ 1 ∈ ℂ | |
3 | 1p1e2 8600 | . 2 ⊢ (1 + 1) = 2 | |
4 | 1, 2, 2, 3 | subaddrii 7832 | 1 ⊢ (2 − 1) = 1 |
Colors of variables: wff set class |
Syntax hints: = wceq 1290 (class class class)co 5666 1c1 7412 − cmin 7714 2c2 8534 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 580 ax-in2 581 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-pow 4015 ax-pr 4045 ax-setind 4366 ax-resscn 7498 ax-1cn 7499 ax-1re 7500 ax-icn 7501 ax-addcl 7502 ax-addrcl 7503 ax-mulcl 7504 ax-addcom 7506 ax-addass 7508 ax-distr 7510 ax-i2m1 7511 ax-0id 7514 ax-rnegex 7515 ax-cnre 7517 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-fal 1296 df-nf 1396 df-sb 1694 df-eu 1952 df-mo 1953 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ne 2257 df-ral 2365 df-rex 2366 df-reu 2367 df-rab 2369 df-v 2622 df-sbc 2842 df-dif 3002 df-un 3004 df-in 3006 df-ss 3013 df-pw 3435 df-sn 3456 df-pr 3457 df-op 3459 df-uni 3660 df-br 3852 df-opab 3906 df-id 4129 df-xp 4458 df-rel 4459 df-cnv 4460 df-co 4461 df-dm 4462 df-iota 4993 df-fun 5030 df-fv 5036 df-riota 5622 df-ov 5669 df-oprab 5670 df-mpt2 5671 df-sub 7716 df-2 8542 |
This theorem is referenced by: 1e2m1 8602 1mhlfehlf 8695 addltmul 8713 xp1d2m1eqxm1d2 8729 nn0lt2 8889 zeo 8912 fzo0to2pr 9690 bcn2 10233 maxabslemlub 10701 geo2sum2 10970 ege2le3 11022 cos2tsin 11103 odd2np1 11212 oddp1even 11215 mod2eq1n2dvds 11218 oddge22np1 11220 ex-fl 11925 |
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