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Mirrors > Home > ILE Home > Th. List > cbvexdh | Unicode version |
Description: Deduction used to change bound variables, using implicit substitition, particularly useful in conjunction with dvelim 2017. (Contributed by NM, 2-Jan-2002.) (Proof rewritten by Jim Kingdon, 30-Dec-2017.) |
Ref | Expression |
---|---|
cbvexdh.1 |
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cbvexdh.2 |
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cbvexdh.3 |
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Ref | Expression |
---|---|
cbvexdh |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1526 |
. . 3
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2 | ax-17 1526 |
. . . 4
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3 | 2 | hbex 1636 |
. . 3
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4 | cbvexdh.1 |
. . . . 5
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5 | cbvexdh.2 |
. . . . 5
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6 | cbvexdh.3 |
. . . . . 6
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7 | equcomi 1704 |
. . . . . . 7
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8 | bicom1 131 |
. . . . . . 7
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9 | 7, 8 | imim12i 59 |
. . . . . 6
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10 | 6, 9 | syl 14 |
. . . . 5
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11 | 4, 5, 10 | equsexd 1729 |
. . . 4
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12 | simpr 110 |
. . . . 5
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13 | 12 | eximi 1600 |
. . . 4
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14 | 11, 13 | syl6bir 164 |
. . 3
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15 | 1, 3, 14 | exlimdh 1596 |
. 2
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16 | 1, 5 | eximdh 1611 |
. . . 4
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17 | 19.12 1665 |
. . . 4
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18 | 16, 17 | syl6 33 |
. . 3
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19 | 2 | a1i 9 |
. . . . 5
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20 | 1, 19, 6 | equsexd 1729 |
. . . 4
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21 | simpr 110 |
. . . . 5
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22 | 21 | eximi 1600 |
. . . 4
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23 | 20, 22 | syl6bir 164 |
. . 3
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24 | 4, 18, 23 | exlimd2 1595 |
. 2
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25 | 15, 24 | 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 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: cbvexd 1927 |
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