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Mirrors > Home > ILE Home > Th. List > spc3gv | Unicode version |
Description: Specialization with 3 quantifiers, using implicit substitution. (Contributed by NM, 12-May-2008.) |
Ref | Expression |
---|---|
spc3egv.1 |
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Ref | Expression |
---|---|
spc3gv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2703 |
. . . 4
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2 | elisset 2703 |
. . . 4
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3 | elisset 2703 |
. . . 4
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4 | 1, 2, 3 | 3anim123i 1167 |
. . 3
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5 | eeeanv 1906 |
. . 3
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6 | 4, 5 | sylibr 133 |
. 2
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7 | spc3egv.1 |
. . . . . . . 8
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8 | 7 | biimpcd 158 |
. . . . . . 7
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9 | 8 | 2alimi 1433 |
. . . . . 6
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10 | 9 | alimi 1432 |
. . . . 5
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11 | exim 1579 |
. . . . . 6
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12 | 11 | 2alimi 1433 |
. . . . 5
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13 | 10, 12 | syl 14 |
. . . 4
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14 | exim 1579 |
. . . . 5
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15 | 14 | alimi 1432 |
. . . 4
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16 | exim 1579 |
. . . 4
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17 | 13, 15, 16 | 3syl 17 |
. . 3
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18 | 19.9v 1844 |
. . . 4
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19 | 19.9v 1844 |
. . . 4
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20 | 19.9v 1844 |
. . . 4
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21 | 18, 19, 20 | 3bitri 205 |
. . 3
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22 | 17, 21 | syl6ib 160 |
. 2
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23 | 6, 22 | syl5com 29 |
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-3an 965 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-v 2691 |
This theorem is referenced by: funopg 5165 |
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