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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1415 | Structured version Visualization version Unicode version |
Description: Technical lemma for bnj60 29919. 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 |
---|---|
bnj1415.1 |
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bnj1415.2 |
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bnj1415.3 |
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bnj1415.4 |
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bnj1415.5 |
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bnj1415.6 |
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bnj1415.7 |
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bnj1415.8 |
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bnj1415.9 |
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bnj1415.10 |
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Ref | Expression |
---|---|
bnj1415 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1415.7 |
. . . 4
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2 | bnj1415.6 |
. . . . 5
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3 | 2 | simplbi 466 |
. . . 4
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4 | 1, 3 | bnj835 29618 |
. . 3
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5 | bnj1415.5 |
. . . 4
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6 | 5, 1 | bnj1212 29659 |
. . 3
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7 | eqid 2461 |
. . . 4
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8 | 7 | bnj1414 29894 |
. . 3
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9 | 4, 6, 8 | syl2anc 671 |
. 2
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10 | iunun 4375 |
. . . 4
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11 | iunid 4346 |
. . . . 5
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12 | 11 | uneq1i 3595 |
. . . 4
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13 | 10, 12 | eqtri 2483 |
. . 3
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14 | bnj1415.1 |
. . . 4
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15 | bnj1415.2 |
. . . 4
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16 | bnj1415.3 |
. . . 4
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17 | bnj1415.4 |
. . . 4
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18 | bnj1415.8 |
. . . 4
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19 | bnj1415.9 |
. . . 4
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20 | bnj1415.10 |
. . . 4
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21 | biid 244 |
. . . 4
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22 | biid 244 |
. . . 4
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23 | 14, 15, 16, 17, 5, 2, 1, 18, 19, 20, 21, 22 | bnj1398 29891 |
. . 3
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24 | 13, 23 | syl5eqr 2509 |
. 2
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25 | 9, 24 | eqtr2d 2496 |
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 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-8 1899 ax-9 1906 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 ax-rep 4528 ax-sep 4538 ax-nul 4547 ax-pow 4594 ax-pr 4652 ax-un 6609 ax-reg 8132 ax-inf2 8171 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3or 992 df-3an 993 df-tru 1457 df-fal 1460 df-ex 1674 df-nf 1678 df-sb 1808 df-eu 2313 df-mo 2314 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-ne 2634 df-ral 2753 df-rex 2754 df-reu 2755 df-rab 2757 df-v 3058 df-sbc 3279 df-csb 3375 df-dif 3418 df-un 3420 df-in 3422 df-ss 3429 df-pss 3431 df-nul 3743 df-if 3893 df-pw 3964 df-sn 3980 df-pr 3982 df-tp 3984 df-op 3986 df-uni 4212 df-iun 4293 df-br 4416 df-opab 4475 df-mpt 4476 df-tr 4511 df-eprel 4763 df-id 4767 df-po 4773 df-so 4774 df-fr 4811 df-we 4813 df-xp 4858 df-rel 4859 df-cnv 4860 df-co 4861 df-dm 4862 df-rn 4863 df-res 4864 df-ima 4865 df-ord 5444 df-on 5445 df-lim 5446 df-suc 5447 df-iota 5564 df-fun 5602 df-fn 5603 df-f 5604 df-f1 5605 df-fo 5606 df-f1o 5607 df-fv 5608 df-om 6719 df-1o 7207 df-bnj17 29540 df-bnj14 29542 df-bnj13 29544 df-bnj15 29546 df-bnj18 29548 df-bnj19 29550 |
This theorem is referenced by: bnj1312 29915 |
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