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Mirrors > Home > ILE Home > Th. List > cgsex4g | Unicode version |
Description: An implicit substitution inference for 4 general classes. (Contributed by NM, 5-Aug-1995.) |
Ref | Expression |
---|---|
cgsex4g.1 |
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cgsex4g.2 |
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Ref | Expression |
---|---|
cgsex4g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cgsex4g.2 |
. . . . 5
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2 | 1 | biimpa 294 |
. . . 4
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3 | 2 | exlimivv 1869 |
. . 3
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4 | 3 | exlimivv 1869 |
. 2
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5 | elisset 2703 |
. . . . . . . 8
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6 | elisset 2703 |
. . . . . . . 8
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7 | 5, 6 | anim12i 336 |
. . . . . . 7
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8 | eeanv 1905 |
. . . . . . 7
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9 | 7, 8 | sylibr 133 |
. . . . . 6
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10 | elisset 2703 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
11 | elisset 2703 |
. . . . . . . 8
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12 | 10, 11 | anim12i 336 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | eeanv 1905 |
. . . . . . 7
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14 | 12, 13 | sylibr 133 |
. . . . . 6
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15 | 9, 14 | anim12i 336 |
. . . . 5
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16 | ee4anv 1907 |
. . . . 5
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17 | 15, 16 | sylibr 133 |
. . . 4
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18 | cgsex4g.1 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
19 | 18 | 2eximi 1581 |
. . . . 5
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20 | 19 | 2eximi 1581 |
. . . 4
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21 | 17, 20 | syl 14 |
. . 3
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22 | 1 | biimprcd 159 |
. . . . . 6
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23 | 22 | ancld 323 |
. . . . 5
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24 | 23 | 2eximdv 1855 |
. . . 4
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25 | 24 | 2eximdv 1855 |
. . 3
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26 | 21, 25 | syl5com 29 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | 4, 26 | impbid2 142 |
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: copsex4g 4177 brecop 6527 |
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