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Mirrors > Home > ILE Home > Th. List > 8th4div3 | Unicode version |
Description: An eighth of four thirds is a sixth. (Contributed by Paul Chapman, 24-Nov-2007.) |
Ref | Expression |
---|---|
8th4div3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1cn 7867 | . . . 4 | |
2 | 8re 8963 | . . . . 5 | |
3 | 2 | recni 7932 | . . . 4 |
4 | 4cn 8956 | . . . 4 | |
5 | 3cn 8953 | . . . 4 | |
6 | 8pos 8981 | . . . . 5 | |
7 | 2, 6 | gt0ap0ii 8547 | . . . 4 # |
8 | 3re 8952 | . . . . 5 | |
9 | 3pos 8972 | . . . . 5 | |
10 | 8, 9 | gt0ap0ii 8547 | . . . 4 # |
11 | 1, 3, 4, 5, 7, 10 | divmuldivapi 8689 | . . 3 |
12 | 1, 4 | mulcomi 7926 | . . . 4 |
13 | 2cn 8949 | . . . . . . . 8 | |
14 | 4, 13, 5 | mul32i 8066 | . . . . . . 7 |
15 | 4t2e8 9036 | . . . . . . . 8 | |
16 | 15 | oveq1i 5863 | . . . . . . 7 |
17 | 14, 16 | eqtr3i 2193 | . . . . . 6 |
18 | 4, 5, 13 | mulassi 7929 | . . . . . 6 |
19 | 17, 18 | eqtr3i 2193 | . . . . 5 |
20 | 3t2e6 9034 | . . . . . 6 | |
21 | 20 | oveq2i 5864 | . . . . 5 |
22 | 19, 21 | eqtri 2191 | . . . 4 |
23 | 12, 22 | oveq12i 5865 | . . 3 |
24 | 11, 23 | eqtri 2191 | . 2 |
25 | 6re 8959 | . . . 4 | |
26 | 25 | recni 7932 | . . 3 |
27 | 6pos 8979 | . . . 4 | |
28 | 25, 27 | gt0ap0ii 8547 | . . 3 # |
29 | 4re 8955 | . . . 4 | |
30 | 4pos 8975 | . . . 4 | |
31 | 29, 30 | gt0ap0ii 8547 | . . 3 # |
32 | divcanap5 8631 | . . . 4 # # | |
33 | 1, 32 | mp3an1 1319 | . . 3 # # |
34 | 26, 28, 4, 31, 33 | mp4an 425 | . 2 |
35 | 24, 34 | eqtri 2191 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1348 wcel 2141 class class class wbr 3989 (class class class)co 5853 cc 7772 cc0 7774 c1 7775 cmul 7779 # cap 8500 cdiv 8589 c2 8929 c3 8930 c4 8931 c6 8933 c8 8935 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 ax-un 4418 ax-setind 4521 ax-cnex 7865 ax-resscn 7866 ax-1cn 7867 ax-1re 7868 ax-icn 7869 ax-addcl 7870 ax-addrcl 7871 ax-mulcl 7872 ax-mulrcl 7873 ax-addcom 7874 ax-mulcom 7875 ax-addass 7876 ax-mulass 7877 ax-distr 7878 ax-i2m1 7879 ax-0lt1 7880 ax-1rid 7881 ax-0id 7882 ax-rnegex 7883 ax-precex 7884 ax-cnre 7885 ax-pre-ltirr 7886 ax-pre-ltwlin 7887 ax-pre-lttrn 7888 ax-pre-apti 7889 ax-pre-ltadd 7890 ax-pre-mulgt0 7891 ax-pre-mulext 7892 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ne 2341 df-nel 2436 df-ral 2453 df-rex 2454 df-reu 2455 df-rmo 2456 df-rab 2457 df-v 2732 df-sbc 2956 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-opab 4051 df-id 4278 df-po 4281 df-iso 4282 df-xp 4617 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-iota 5160 df-fun 5200 df-fv 5206 df-riota 5809 df-ov 5856 df-oprab 5857 df-mpo 5858 df-pnf 7956 df-mnf 7957 df-xr 7958 df-ltxr 7959 df-le 7960 df-sub 8092 df-neg 8093 df-reap 8494 df-ap 8501 df-div 8590 df-2 8937 df-3 8938 df-4 8939 df-5 8940 df-6 8941 df-7 8942 df-8 8943 |
This theorem is referenced by: (None) |
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