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Mirrors > Home > ILE Home > Th. List > vtoclgft | Unicode version |
Description: Closed theorem form of vtoclgf 2810. (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 2763 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | elisset 2766 |
. . . . 5
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3 | 2 | 3ad2ant3 1022 |
. . . 4
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4 | nfnfc1 2335 |
. . . . . . 7
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5 | nfcvd 2333 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | id 19 |
. . . . . . . 8
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7 | 5, 6 | nfeqd 2347 |
. . . . . . 7
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8 | eqeq1 2196 |
. . . . . . . 8
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9 | 8 | a1i 9 |
. . . . . . 7
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10 | 4, 7, 9 | cbvexd 1939 |
. . . . . 6
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11 | 10 | ad2antrr 488 |
. . . . 5
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12 | 11 | 3adant3 1019 |
. . . 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 1470 |
. . . . 5
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19 | 18 | 3ad2ant2 1021 |
. . . 4
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20 | simp1r 1024 |
. . . . 5
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21 | 19.23t 1688 |
. . . . 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 1284 |
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 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-v 2754 |
This theorem is referenced by: vtocldf 2803 |
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