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Mirrors > Home > ILE Home > Th. List > vtoclgft | Unicode version |
Description: Closed theorem form of vtoclgf 2807. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
vtoclgft |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2760 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | elisset 2763 |
. . . . 5
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3 | 2 | 3ad2ant3 1021 |
. . . 4
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4 | nfnfc1 2332 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() | |
5 | nfcvd 2330 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | id 19 |
. . . . . . . 8
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7 | 5, 6 | nfeqd 2344 |
. . . . . . 7
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8 | eqeq1 2194 |
. . . . . . . 8
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9 | 8 | a1i 9 |
. . . . . . 7
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10 | 4, 7, 9 | cbvexd 1937 |
. . . . . 6
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11 | 10 | ad2antrr 488 |
. . . . 5
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12 | 11 | 3adant3 1018 |
. . . 4
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13 | 3, 12 | mpbid 147 |
. . 3
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14 | biimp 118 |
. . . . . . . . 9
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15 | 14 | imim2i 12 |
. . . . . . . 8
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16 | 15 | com23 78 |
. . . . . . 7
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17 | 16 | imp 124 |
. . . . . 6
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18 | 17 | alanimi 1469 |
. . . . 5
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19 | 18 | 3ad2ant2 1020 |
. . . 4
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20 | simp1r 1023 |
. . . . 5
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21 | 19.23t 1687 |
. . . . 5
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22 | 20, 21 | syl 14 |
. . . 4
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23 | 19, 22 | mpbid 147 |
. . 3
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24 | 13, 23 | mpd 13 |
. 2
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25 | 1, 24 | syl3an3 1283 |
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 106 ax-ia2 107 ax-ia3 108 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-v 2751 |
This theorem is referenced by: vtocldf 2800 |
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