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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 1643 |
. 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 465 |
. . . . . 6
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6 | 5 | bicomd 140 |
. . . . 5
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7 | 6 | eqcoms 2143 |
. . . 4
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8 | 2, 7 | ceqsexv 2728 |
. . 3
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9 | 8 | exbii 1585 |
. 2
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10 | 19.41v 1875 |
. . . 4
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11 | simpr 109 |
. . . . 5
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12 | gencbvex.4 |
. . . . . . . 8
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13 | eqcom 2142 |
. . . . . . . . . . 11
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14 | 13 | biimpi 119 |
. . . . . . . . . 10
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15 | 14 | adantl 275 |
. . . . . . . . 9
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16 | 15 | eximi 1580 |
. . . . . . . 8
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17 | 12, 16 | sylbi 120 |
. . . . . . 7
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18 | 17 | adantr 274 |
. . . . . 6
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19 | 18 | ancri 322 |
. . . . 5
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20 | 11, 19 | impbii 125 |
. . . 4
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21 | 10, 20 | bitri 183 |
. . 3
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22 | 21 | exbii 1585 |
. 2
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23 | 1, 9, 22 | 3bitr3i 209 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-v 2691 |
This theorem is referenced by: gencbvex2 2736 |
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