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Mirrors > Home > ILE Home > Th. List > csbiebt | Unicode version |
Description: Conversion of implicit substitution to explicit substitution into a class. (Closed theorem version of csbiegf 3048.) (Contributed by NM, 11-Nov-2005.) |
Ref | Expression |
---|---|
csbiebt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2700 |
. 2
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2 | spsbc 2924 |
. . . . 5
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3 | 2 | adantr 274 |
. . . 4
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4 | simpl 108 |
. . . . 5
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5 | biimt 240 |
. . . . . . 7
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6 | csbeq1a 3016 |
. . . . . . . 8
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7 | 6 | eqeq1d 2149 |
. . . . . . 7
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8 | 5, 7 | bitr3d 189 |
. . . . . 6
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9 | 8 | adantl 275 |
. . . . 5
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10 | nfv 1509 |
. . . . . 6
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11 | nfnfc1 2285 |
. . . . . 6
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12 | 10, 11 | nfan 1545 |
. . . . 5
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13 | nfcsb1v 3040 |
. . . . . . 7
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14 | 13 | a1i 9 |
. . . . . 6
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15 | simpr 109 |
. . . . . 6
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16 | 14, 15 | nfeqd 2297 |
. . . . 5
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17 | 4, 9, 12, 16 | sbciedf 2948 |
. . . 4
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18 | 3, 17 | sylibd 148 |
. . 3
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19 | 13 | a1i 9 |
. . . . . . . 8
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20 | id 19 |
. . . . . . . 8
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21 | 19, 20 | nfeqd 2297 |
. . . . . . 7
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22 | 11, 21 | nfan1 1544 |
. . . . . 6
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23 | 7 | biimprcd 159 |
. . . . . . 7
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24 | 23 | adantl 275 |
. . . . . 6
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25 | 22, 24 | alrimi 1503 |
. . . . 5
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26 | 25 | ex 114 |
. . . 4
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27 | 26 | adantl 275 |
. . 3
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28 | 18, 27 | impbid 128 |
. 2
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29 | 1, 28 | sylan 281 |
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-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-sbc 2914 df-csb 3008 |
This theorem is referenced by: csbiedf 3045 csbieb 3046 csbiegf 3048 |
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