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Mirrors > Home > ILE Home > Th. List > gencbvex | Unicode version |
Description: Change of bound variable using implicit substitution. (Contributed by NM, 17-May-1996.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
gencbvex.1 |
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gencbvex.2 |
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gencbvex.3 |
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gencbvex.4 |
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Ref | Expression |
---|---|
gencbvex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 1551 |
. 2
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2 | gencbvex.1 |
. . . 4
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3 | gencbvex.3 |
. . . . . . 7
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4 | gencbvex.2 |
. . . . . . 7
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5 | 3, 4 | anbi12d 442 |
. . . . . 6
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6 | 5 | bicomd 129 |
. . . . 5
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7 | 6 | eqcoms 2040 |
. . . 4
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8 | 2, 7 | ceqsexv 2587 |
. . 3
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9 | 8 | exbii 1493 |
. 2
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10 | 19.41v 1779 |
. . . 4
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11 | simpr 103 |
. . . . 5
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12 | gencbvex.4 |
. . . . . . . 8
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13 | eqcom 2039 |
. . . . . . . . . . 11
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14 | 13 | biimpi 113 |
. . . . . . . . . 10
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15 | 14 | adantl 262 |
. . . . . . . . 9
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16 | 15 | eximi 1488 |
. . . . . . . 8
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17 | 12, 16 | sylbi 114 |
. . . . . . 7
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18 | 17 | adantr 261 |
. . . . . 6
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19 | 18 | ancri 307 |
. . . . 5
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20 | 11, 19 | impbii 117 |
. . . 4
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21 | 10, 20 | bitri 173 |
. . 3
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22 | 21 | exbii 1493 |
. 2
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23 | 1, 9, 22 | 3bitr3i 199 |
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 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-v 2553 |
This theorem is referenced by: gencbvex2 2595 |
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