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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1177 | Structured version Visualization version Unicode version |
Description: Technical lemma for bnj69 29891. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj1177.2 |
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bnj1177.3 |
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bnj1177.9 |
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bnj1177.13 |
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bnj1177.17 |
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Ref | Expression |
---|---|
bnj1177 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1177.9 |
. . 3
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2 | df-bnj15 29570 |
. . . 4
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3 | 2 | simplbi 467 |
. . 3
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4 | 1, 3 | syl 17 |
. 2
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5 | bnj1177.3 |
. . . 4
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6 | bnj1147 29875 |
. . . . 5
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7 | ssinss1 3651 |
. . . . 5
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8 | 6, 7 | ax-mp 5 |
. . . 4
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9 | 5, 8 | eqsstri 3448 |
. . 3
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10 | 9 | a1i 11 |
. 2
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11 | bnj1177.17 |
. . . . . . 7
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12 | bnj906 29813 |
. . . . . . 7
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13 | 1, 11, 12 | syl2anc 673 |
. . . . . 6
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14 | ssrin 3648 |
. . . . . 6
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15 | 13, 14 | syl 17 |
. . . . 5
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16 | bnj1177.13 |
. . . . . . . 8
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17 | bnj1177.2 |
. . . . . . . . . 10
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18 | 17 | simp2bi 1046 |
. . . . . . . . 9
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19 | 18 | adantl 473 |
. . . . . . . 8
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20 | 16, 19 | sseldd 3419 |
. . . . . . 7
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21 | 17 | simp3bi 1047 |
. . . . . . . 8
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22 | 21 | adantl 473 |
. . . . . . 7
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23 | bnj1152 29879 |
. . . . . . 7
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24 | 20, 22, 23 | sylanbrc 677 |
. . . . . 6
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25 | 24, 19 | elind 3609 |
. . . . 5
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26 | 15, 25 | sseldd 3419 |
. . . 4
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27 | ne0i 3728 |
. . . 4
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28 | 26, 27 | syl 17 |
. . 3
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29 | 5 | neeq1i 2707 |
. . 3
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30 | 28, 29 | sylibr 217 |
. 2
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31 | bnj893 29811 |
. . . 4
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32 | 1, 11, 31 | syl2anc 673 |
. . 3
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33 | inex1g 4539 |
. . . 4
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34 | 5, 33 | syl5eqel 2553 |
. . 3
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35 | 32, 34 | syl 17 |
. 2
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36 | 4, 10, 30, 35 | bnj951 29659 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-8 1906 ax-9 1913 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 ax-rep 4508 ax-sep 4518 ax-nul 4527 ax-pow 4579 ax-pr 4639 ax-un 6602 ax-reg 8125 ax-inf2 8164 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3or 1008 df-3an 1009 df-tru 1455 df-fal 1458 df-ex 1672 df-nf 1676 df-sb 1806 df-eu 2323 df-mo 2324 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ne 2643 df-ral 2761 df-rex 2762 df-reu 2763 df-rab 2765 df-v 3033 df-sbc 3256 df-csb 3350 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-pss 3406 df-nul 3723 df-if 3873 df-pw 3944 df-sn 3960 df-pr 3962 df-tp 3964 df-op 3966 df-uni 4191 df-iun 4271 df-br 4396 df-opab 4455 df-mpt 4456 df-tr 4491 df-eprel 4750 df-id 4754 df-po 4760 df-so 4761 df-fr 4798 df-we 4800 df-xp 4845 df-rel 4846 df-cnv 4847 df-co 4848 df-dm 4849 df-rn 4850 df-res 4851 df-ima 4852 df-ord 5433 df-on 5434 df-lim 5435 df-suc 5436 df-iota 5553 df-fun 5591 df-fn 5592 df-f 5593 df-f1 5594 df-fo 5595 df-f1o 5596 df-fv 5597 df-om 6712 df-1o 7200 df-bnj17 29564 df-bnj14 29566 df-bnj13 29568 df-bnj15 29570 df-bnj18 29572 |
This theorem is referenced by: bnj1190 29889 |
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