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Mirrors > Home > ILE Home > Th. List > equsexd | Unicode version |
Description: Deduction form of equsex 1738. (Contributed by Jim Kingdon, 29-Dec-2017.) |
Ref | Expression |
---|---|
equsexd.1 |
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equsexd.2 |
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equsexd.3 |
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Ref | Expression |
---|---|
equsexd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equsexd.1 |
. . 3
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2 | equsexd.2 |
. . 3
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3 | equsexd.3 |
. . . 4
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4 | biimp 118 |
. . . . 5
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5 | 4 | imim2i 12 |
. . . 4
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6 | pm3.31 262 |
. . . 4
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7 | 3, 5, 6 | 3syl 17 |
. . 3
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8 | 1, 2, 7 | exlimd2 1605 |
. 2
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9 | a9e 1706 |
. . . 4
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10 | 1 | a1i 9 |
. . . . . . . . 9
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11 | 10, 2 | jca 306 |
. . . . . . . 8
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12 | anim12 344 |
. . . . . . . 8
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13 | 11, 12 | syl 14 |
. . . . . . 7
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14 | 19.26 1491 |
. . . . . . 7
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15 | 13, 14 | imbitrrdi 162 |
. . . . . 6
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16 | 15 | anabsi5 579 |
. . . . 5
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17 | idd 21 |
. . . . . . . 8
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18 | 17 | a1i 9 |
. . . . . . 7
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19 | 18 | imp 124 |
. . . . . 6
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20 | biimpr 130 |
. . . . . . . . 9
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21 | 20 | imim2i 12 |
. . . . . . . 8
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22 | pm2.04 82 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
23 | 3, 21, 22 | 3syl 17 |
. . . . . . 7
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24 | 23 | imp 124 |
. . . . . 6
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25 | 19, 24 | jcad 307 |
. . . . 5
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26 | 16, 25 | eximdh 1621 |
. . . 4
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27 | 9, 26 | mpi 15 |
. . 3
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28 | 27 | ex 115 |
. 2
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29 | 8, 28 | impbid 129 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1457 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-4 1520 ax-i9 1540 ax-ial 1544 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: cbvexdh 1936 |
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