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Mirrors > Home > ILE Home > Th. List > gencbval | Unicode version |
Description: Change of bound variable using implicit substitution. (Contributed by NM, 17-May-1996.) (Proof rewritten by Jim Kingdon, 20-Jun-2018.) |
Ref | Expression |
---|---|
gencbval.1 |
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gencbval.2 |
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gencbval.3 |
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gencbval.4 |
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Ref | Expression |
---|---|
gencbval |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alcom 1408 |
. 2
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2 | gencbval.1 |
. . . 4
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3 | gencbval.3 |
. . . . . . 7
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4 | gencbval.2 |
. . . . . . 7
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5 | 3, 4 | imbi12d 232 |
. . . . . 6
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6 | 5 | bicomd 139 |
. . . . 5
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7 | 6 | eqcoms 2086 |
. . . 4
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8 | 2, 7 | ceqsalv 2640 |
. . 3
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9 | 8 | albii 1400 |
. 2
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10 | 19.23v 1806 |
. . . 4
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11 | gencbval.4 |
. . . . . . 7
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12 | eqcom 2085 |
. . . . . . . . . 10
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13 | 12 | biimpi 118 |
. . . . . . . . 9
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14 | 13 | adantl 271 |
. . . . . . . 8
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15 | 14 | eximi 1532 |
. . . . . . 7
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16 | 11, 15 | sylbi 119 |
. . . . . 6
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17 | pm2.04 81 |
. . . . . 6
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18 | 16, 17 | mpdi 42 |
. . . . 5
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19 | ax-1 5 |
. . . . 5
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20 | 18, 19 | impbii 124 |
. . . 4
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21 | 10, 20 | bitri 182 |
. . 3
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22 | 21 | albii 1400 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 1, 9, 22 | 3bitr3i 208 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-ext 2065 |
This theorem depends on definitions: df-bi 115 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-v 2614 |
This theorem is referenced by: (None) |
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