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Mirrors > Home > MPE Home > Th. List > Mathboxes > nobndlem8 | Structured version Visualization version Unicode version |
Description: Lemma for nobndup 30601 and nobnddown 30602. Bound the birthday of
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Ref | Expression |
---|---|
nobndlem8.1 |
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nobndlem8.2 |
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Ref | Expression |
---|---|
nobndlem8 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 3056 |
. 2
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2 | nobndlem8.1 |
. . . . 5
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3 | nobndlem8.2 |
. . . . 5
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4 | 2, 3 | nobndlem3 30595 |
. . . 4
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5 | 4, 3 | syl6eq 2503 |
. . 3
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6 | nobndlem1 30593 |
. . . . 5
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7 | 6 | adantl 468 |
. . . 4
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8 | bdayfn 30580 |
. . . . . . . . . . 11
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9 | fnfvima 6148 |
. . . . . . . . . . 11
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10 | 8, 9 | mp3an1 1353 |
. . . . . . . . . 10
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11 | 10 | 3adant2 1028 |
. . . . . . . . 9
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12 | elssuni 4230 |
. . . . . . . . 9
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13 | 11, 12 | syl 17 |
. . . . . . . 8
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14 | bdayelon 30581 |
. . . . . . . . 9
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15 | sucelon 6649 |
. . . . . . . . . . 11
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16 | 6, 15 | sylibr 216 |
. . . . . . . . . 10
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17 | 16 | 3ad2ant2 1031 |
. . . . . . . . 9
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18 | onsssuc 5513 |
. . . . . . . . 9
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19 | 14, 17, 18 | sylancr 670 |
. . . . . . . 8
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20 | 13, 19 | mpbid 214 |
. . . . . . 7
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21 | ssel2 3429 |
. . . . . . . . 9
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22 | fvnobday 30583 |
. . . . . . . . . 10
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23 | 2 | nosgnn0i 30558 |
. . . . . . . . . . 11
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24 | 23 | a1i 11 |
. . . . . . . . . 10
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25 | 22, 24 | eqnetrd 2693 |
. . . . . . . . 9
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26 | 21, 25 | syl 17 |
. . . . . . . 8
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27 | 26 | 3adant2 1028 |
. . . . . . 7
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28 | fveq2 5870 |
. . . . . . . . 9
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29 | 28 | neeq1d 2685 |
. . . . . . . 8
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30 | 29 | rspcev 3152 |
. . . . . . 7
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31 | 20, 27, 30 | syl2anc 667 |
. . . . . 6
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32 | 31 | 3expa 1209 |
. . . . 5
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33 | 32 | ralrimiva 2804 |
. . . 4
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34 | rexeq 2990 |
. . . . . 6
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35 | 34 | ralbidv 2829 |
. . . . 5
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36 | 35 | intminss 4264 |
. . . 4
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37 | 7, 33, 36 | syl2anc 667 |
. . 3
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38 | 5, 37 | eqsstrd 3468 |
. 2
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39 | 1, 38 | sylan2 477 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-8 1891 ax-9 1898 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 ax-rep 4518 ax-sep 4528 ax-nul 4537 ax-pow 4584 ax-pr 4642 ax-un 6588 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 987 df-3an 988 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-eu 2305 df-mo 2306 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-ne 2626 df-ral 2744 df-rex 2745 df-reu 2746 df-rab 2748 df-v 3049 df-sbc 3270 df-csb 3366 df-dif 3409 df-un 3411 df-in 3413 df-ss 3420 df-pss 3422 df-nul 3734 df-if 3884 df-pw 3955 df-sn 3971 df-pr 3973 df-tp 3975 df-op 3977 df-uni 4202 df-int 4238 df-iun 4283 df-br 4406 df-opab 4465 df-mpt 4466 df-tr 4501 df-eprel 4748 df-id 4752 df-po 4758 df-so 4759 df-fr 4796 df-we 4798 df-xp 4843 df-rel 4844 df-cnv 4845 df-co 4846 df-dm 4847 df-rn 4848 df-res 4849 df-ima 4850 df-ord 5429 df-on 5430 df-suc 5432 df-iota 5549 df-fun 5587 df-fn 5588 df-f 5589 df-f1 5590 df-fo 5591 df-f1o 5592 df-fv 5593 df-1o 7187 df-2o 7188 df-no 30542 df-bday 30544 |
This theorem is referenced by: nobndup 30601 nobnddown 30602 |
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