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Mirrors > Home > MPE Home > Th. List > kmlem4 | Structured version Visualization version Unicode version |
Description: Lemma for 5-quantifier AC of Kurt Maes, Th. 4, part of 3 => 4. (Contributed by NM, 26-Mar-2004.) |
Ref | Expression |
---|---|
kmlem4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldif 3414 |
. . . . 5
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2 | simpr 463 |
. . . . . 6
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3 | eluni 4201 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 3 | notbii 298 |
. . . . . . 7
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5 | alnex 1665 |
. . . . . . 7
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6 | con2b 336 |
. . . . . . . . 9
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7 | imnan 424 |
. . . . . . . . 9
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8 | eldifsn 4097 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | necom 2677 |
. . . . . . . . . . . 12
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10 | 9 | anbi2i 700 |
. . . . . . . . . . 11
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11 | 8, 10 | bitri 253 |
. . . . . . . . . 10
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12 | 11 | imbi1i 327 |
. . . . . . . . 9
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13 | 6, 7, 12 | 3bitr3i 279 |
. . . . . . . 8
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14 | 13 | albii 1691 |
. . . . . . 7
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15 | 4, 5, 14 | 3bitr2i 277 |
. . . . . 6
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16 | 2, 15 | sylib 200 |
. . . . 5
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17 | 1, 16 | sylbi 199 |
. . . 4
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18 | eleq1 2517 |
. . . . . . . 8
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19 | neeq2 2687 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
20 | 18, 19 | anbi12d 717 |
. . . . . . 7
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21 | eleq2 2518 |
. . . . . . . 8
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22 | 21 | notbid 296 |
. . . . . . 7
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23 | 20, 22 | imbi12d 322 |
. . . . . 6
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24 | 23 | spv 2104 |
. . . . 5
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25 | 24 | com12 32 |
. . . 4
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26 | 17, 25 | syl5 33 |
. . 3
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27 | 26 | ralrimiv 2800 |
. 2
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28 | disj 3805 |
. 2
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29 | 27, 28 | sylibr 216 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 189 df-an 373 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-v 3047 df-dif 3407 df-in 3411 df-nul 3732 df-sn 3969 df-uni 4199 |
This theorem is referenced by: kmlem5 8584 kmlem11 8590 |
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