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Mirrors > Home > ILE Home > Th. List > 3m1e2 | GIF version |
Description: 3 - 1 = 2. (Contributed by FL, 17-Oct-2010.) (Revised by NM, 10-Dec-2017.) |
Ref | Expression |
---|---|
3m1e2 | ⊢ (3 − 1) = 2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3cn 8983 | . 2 ⊢ 3 ∈ ℂ | |
2 | ax-1cn 7895 | . 2 ⊢ 1 ∈ ℂ | |
3 | 2cn 8979 | . 2 ⊢ 2 ∈ ℂ | |
4 | 2, 3 | addcomi 8091 | . . 3 ⊢ (1 + 2) = (2 + 1) |
5 | df-3 8968 | . . 3 ⊢ 3 = (2 + 1) | |
6 | 4, 5 | eqtr4i 2201 | . 2 ⊢ (1 + 2) = 3 |
7 | 1, 2, 3, 6 | subaddrii 8236 | 1 ⊢ (3 − 1) = 2 |
Colors of variables: wff set class |
Syntax hints: = wceq 1353 (class class class)co 5869 1c1 7803 + caddc 7805 − cmin 8118 2c2 8959 3c3 8960 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4206 ax-setind 4533 ax-resscn 7894 ax-1cn 7895 ax-1re 7896 ax-icn 7897 ax-addcl 7898 ax-addrcl 7899 ax-mulcl 7900 ax-addcom 7902 ax-addass 7904 ax-distr 7906 ax-i2m1 7907 ax-0id 7910 ax-rnegex 7911 ax-cnre 7913 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-reu 2462 df-rab 2464 df-v 2739 df-sbc 2963 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-id 4290 df-xp 4629 df-rel 4630 df-cnv 4631 df-co 4632 df-dm 4633 df-iota 5174 df-fun 5214 df-fv 5220 df-riota 5825 df-ov 5872 df-oprab 5873 df-mpo 5874 df-sub 8120 df-2 8967 df-3 8968 |
This theorem is referenced by: halfpm6th 9128 ige3m2fz 10035 fzo0to3tp 10205 fldiv4p1lem1div2 10291 n2dvds3 11903 3prm 12111 ex-bc 14137 |
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