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Mirrors > Home > ILE Home > Th. List > ex-fl | Unicode version |
Description: Example for df-fl 9826. Example by David A. Wheeler. (Contributed by Mario Carneiro, 18-Jun-2015.) |
Ref | Expression |
---|---|
ex-fl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1re 7584 |
. . . 4
![]() ![]() ![]() ![]() | |
2 | 3re 8594 |
. . . . 5
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3 | 2 | rehalfcli 8762 |
. . . 4
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4 | 2cn 8591 |
. . . . . . 7
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5 | 4 | mulid2i 7588 |
. . . . . 6
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6 | 2lt3 8684 |
. . . . . 6
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7 | 5, 6 | eqbrtri 3886 |
. . . . 5
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8 | 2pos 8611 |
. . . . . 6
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9 | 2re 8590 |
. . . . . . 7
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10 | 1, 2, 9 | ltmuldivi 8480 |
. . . . . 6
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11 | 8, 10 | ax-mp 7 |
. . . . 5
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12 | 7, 11 | mpbi 144 |
. . . 4
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13 | 1, 3, 12 | ltleii 7684 |
. . 3
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14 | 3lt4 8686 |
. . . . . 6
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15 | 2t2e4 8668 |
. . . . . 6
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16 | 14, 15 | breqtrri 3892 |
. . . . 5
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17 | 9, 8 | pm3.2i 267 |
. . . . . 6
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18 | ltdivmul 8434 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
19 | 2, 9, 17, 18 | mp3an 1280 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | 16, 19 | mpbir 145 |
. . . 4
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21 | df-2 8579 |
. . . 4
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22 | 20, 21 | breqtri 3890 |
. . 3
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23 | 3z 8877 |
. . . . 5
![]() ![]() ![]() ![]() | |
24 | 2nn 8675 |
. . . . 5
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25 | znq 9208 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
26 | 23, 24, 25 | mp2an 418 |
. . . 4
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27 | 1z 8874 |
. . . 4
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28 | flqbi 9846 |
. . . 4
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29 | 26, 27, 28 | mp2an 418 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
30 | 13, 22, 29 | mpbir2an 891 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
31 | 9 | renegcli 7841 |
. . . 4
![]() ![]() ![]() ![]() ![]() |
32 | 3 | renegcli 7841 |
. . . 4
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33 | 3, 9 | ltnegi 8068 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
34 | 20, 33 | mpbi 144 |
. . . 4
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35 | 31, 32, 34 | ltleii 7684 |
. . 3
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36 | 4 | negcli 7847 |
. . . . . . 7
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37 | ax-1cn 7535 |
. . . . . . 7
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38 | negdi2 7837 |
. . . . . . 7
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39 | 36, 37, 38 | mp2an 418 |
. . . . . 6
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40 | 4 | negnegi 7849 |
. . . . . . 7
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41 | 40 | oveq1i 5700 |
. . . . . 6
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42 | 39, 41 | eqtri 2115 |
. . . . 5
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43 | 2m1e1 8638 |
. . . . . 6
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44 | 43, 12 | eqbrtri 3886 |
. . . . 5
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45 | 42, 44 | eqbrtri 3886 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
46 | 31, 1 | readdcli 7598 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
47 | 46, 3 | ltnegcon1i 8074 |
. . . 4
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48 | 45, 47 | mpbi 144 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
49 | qnegcl 9220 |
. . . . 5
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50 | 26, 49 | ax-mp 7 |
. . . 4
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51 | 2z 8876 |
. . . . 5
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52 | znegcl 8879 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
53 | 51, 52 | ax-mp 7 |
. . . 4
![]() ![]() ![]() ![]() ![]() |
54 | flqbi 9846 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
55 | 50, 53, 54 | mp2an 418 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
56 | 35, 48, 55 | mpbir2an 891 |
. 2
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57 | 30, 56 | pm3.2i 267 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 582 ax-in2 583 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-13 1456 ax-14 1457 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-sep 3978 ax-pow 4030 ax-pr 4060 ax-un 4284 ax-setind 4381 ax-cnex 7533 ax-resscn 7534 ax-1cn 7535 ax-1re 7536 ax-icn 7537 ax-addcl 7538 ax-addrcl 7539 ax-mulcl 7540 ax-mulrcl 7541 ax-addcom 7542 ax-mulcom 7543 ax-addass 7544 ax-mulass 7545 ax-distr 7546 ax-i2m1 7547 ax-0lt1 7548 ax-1rid 7549 ax-0id 7550 ax-rnegex 7551 ax-precex 7552 ax-cnre 7553 ax-pre-ltirr 7554 ax-pre-ltwlin 7555 ax-pre-lttrn 7556 ax-pre-apti 7557 ax-pre-ltadd 7558 ax-pre-mulgt0 7559 ax-pre-mulext 7560 ax-arch 7561 |
This theorem depends on definitions: df-bi 116 df-3or 928 df-3an 929 df-tru 1299 df-fal 1302 df-nf 1402 df-sb 1700 df-eu 1958 df-mo 1959 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ne 2263 df-nel 2358 df-ral 2375 df-rex 2376 df-reu 2377 df-rmo 2378 df-rab 2379 df-v 2635 df-sbc 2855 df-csb 2948 df-dif 3015 df-un 3017 df-in 3019 df-ss 3026 df-pw 3451 df-sn 3472 df-pr 3473 df-op 3475 df-uni 3676 df-int 3711 df-iun 3754 df-br 3868 df-opab 3922 df-mpt 3923 df-id 4144 df-po 4147 df-iso 4148 df-xp 4473 df-rel 4474 df-cnv 4475 df-co 4476 df-dm 4477 df-rn 4478 df-res 4479 df-ima 4480 df-iota 5014 df-fun 5051 df-fn 5052 df-f 5053 df-fv 5057 df-riota 5646 df-ov 5693 df-oprab 5694 df-mpt2 5695 df-1st 5949 df-2nd 5950 df-pnf 7621 df-mnf 7622 df-xr 7623 df-ltxr 7624 df-le 7625 df-sub 7752 df-neg 7753 df-reap 8149 df-ap 8156 df-div 8237 df-inn 8521 df-2 8579 df-3 8580 df-4 8581 df-n0 8772 df-z 8849 df-q 9204 df-rp 9234 df-fl 9826 |
This theorem is referenced by: ex-ceil 12361 |
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