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Mirrors > Home > ILE Home > Th. List > maxleim | Unicode version |
Description: Value of maximum when we know which number is larger. (Contributed by Jim Kingdon, 21-Dec-2021.) |
Ref | Expression |
---|---|
maxleim |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lttri3 7761 |
. . . 4
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2 | 1 | adantl 273 |
. . 3
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3 | simplr 502 |
. . 3
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4 | prid2g 3592 |
. . . 4
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5 | 3, 4 | syl 14 |
. . 3
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6 | simpll 501 |
. . . . . . 7
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7 | 6 | ad2antrr 477 |
. . . . . 6
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8 | 3 | ad2antrr 477 |
. . . . . 6
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9 | simpllr 506 |
. . . . . 6
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10 | 7, 8, 9 | lensymd 7801 |
. . . . 5
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11 | breq2 3897 |
. . . . . . 7
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12 | 11 | notbid 639 |
. . . . . 6
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13 | 12 | adantl 273 |
. . . . 5
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14 | 10, 13 | mpbird 166 |
. . . 4
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15 | 3 | ad2antrr 477 |
. . . . . 6
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16 | 15 | ltnrd 7792 |
. . . . 5
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17 | breq2 3897 |
. . . . . . 7
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18 | 17 | notbid 639 |
. . . . . 6
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19 | 18 | adantl 273 |
. . . . 5
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20 | 16, 19 | mpbird 166 |
. . . 4
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21 | elpri 3514 |
. . . . 5
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22 | 21 | adantl 273 |
. . . 4
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23 | 14, 20, 22 | mpjaodan 770 |
. . 3
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24 | 2, 3, 5, 23 | supmaxti 6841 |
. 2
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25 | 24 | ex 114 |
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 586 ax-in2 587 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-13 1472 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-pow 4056 ax-pr 4089 ax-un 4313 ax-setind 4410 ax-cnex 7630 ax-resscn 7631 ax-pre-ltirr 7651 ax-pre-apti 7654 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-fal 1318 df-nf 1418 df-sb 1717 df-eu 1976 df-mo 1977 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ne 2281 df-nel 2376 df-ral 2393 df-rex 2394 df-reu 2395 df-rmo 2396 df-rab 2397 df-v 2657 df-sbc 2877 df-dif 3037 df-un 3039 df-in 3041 df-ss 3048 df-pw 3476 df-sn 3497 df-pr 3498 df-op 3500 df-uni 3701 df-br 3894 df-opab 3948 df-xp 4503 df-cnv 4505 df-iota 5044 df-riota 5682 df-sup 6821 df-pnf 7720 df-mnf 7721 df-xr 7722 df-ltxr 7723 df-le 7724 |
This theorem is referenced by: maxleb 10874 xrmaxiflemab 10902 |
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