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Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-ax11-lem8 | Structured version Visualization version Unicode version |
Description: Lemma. (Contributed by Wolf Lammen, 30-Jun-2019.) |
Ref | Expression |
---|---|
wl-ax11-lem8 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axc11n 2157 |
. . 3
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2 | 1 | con3i 142 |
. 2
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3 | wl-ax11-lem1 31979 |
. . . . . . 7
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4 | 3 | notbid 301 |
. . . . . 6
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5 | 4 | anbi1d 719 |
. . . . 5
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6 | 4 | anbi1d 719 |
. . . . . . . 8
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7 | axc11n 2157 |
. . . . . . . . . . 11
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8 | 7 | con3i 142 |
. . . . . . . . . 10
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9 | wl-ax11-lem4 31982 |
. . . . . . . . . . . 12
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10 | sbequ12 2098 |
. . . . . . . . . . . . . . 15
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11 | 10 | equcoms 1872 |
. . . . . . . . . . . . . 14
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12 | 11 | sps 1963 |
. . . . . . . . . . . . 13
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13 | 12 | adantr 472 |
. . . . . . . . . . . 12
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14 | 9, 13 | albid 1983 |
. . . . . . . . . . 11
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15 | 14 | ex 441 |
. . . . . . . . . 10
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16 | 8, 15 | syl5 32 |
. . . . . . . . 9
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17 | 16 | pm5.32d 651 |
. . . . . . . 8
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18 | 6, 17 | bitr4d 264 |
. . . . . . 7
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19 | 18 | dral1 2174 |
. . . . . 6
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20 | wl-ax11-lem7 31985 |
. . . . . 6
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21 | wl-ax11-lem7 31985 |
. . . . . 6
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22 | 19, 20, 21 | 3bitr3g 295 |
. . . . 5
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23 | 5, 22 | bitr3d 263 |
. . . 4
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24 | pm5.32 648 |
. . . 4
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25 | 23, 24 | sylibr 217 |
. . 3
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26 | 25 | imp 436 |
. 2
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27 | 2, 26 | sylan2 482 |
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-10 1932 ax-12 1950 ax-13 2104 ax-wl-11v 31978 |
This theorem depends on definitions: df-bi 190 df-an 378 df-ex 1672 df-nf 1676 df-sb 1806 |
This theorem is referenced by: wl-ax11-lem10 31988 |
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