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Mirrors > Home > ILE Home > Th. List > vtoclgft | Unicode version |
Description: Closed theorem form of vtoclgf 2606. (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 2560 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | elisset 2562 |
. . . . 5
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3 | 2 | 3ad2ant3 926 |
. . . 4
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4 | nfnfc1 2178 |
. . . . . . 7
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5 | nfcvd 2176 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | id 19 |
. . . . . . . 8
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7 | 5, 6 | nfeqd 2189 |
. . . . . . 7
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8 | eqeq1 2043 |
. . . . . . . 8
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9 | 8 | a1i 9 |
. . . . . . 7
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10 | 4, 7, 9 | cbvexd 1799 |
. . . . . 6
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11 | 10 | ad2antrr 457 |
. . . . 5
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12 | 11 | 3adant3 923 |
. . . 4
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13 | 3, 12 | mpbid 135 |
. . 3
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14 | bi1 111 |
. . . . . . . . 9
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15 | 14 | imim2i 12 |
. . . . . . . 8
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16 | 15 | com23 72 |
. . . . . . 7
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17 | 16 | imp 115 |
. . . . . 6
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18 | 17 | alanimi 1345 |
. . . . 5
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19 | 18 | 3ad2ant2 925 |
. . . 4
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20 | simp1r 928 |
. . . . 5
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21 | 19.23t 1564 |
. . . . 5
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22 | 20, 21 | syl 14 |
. . . 4
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23 | 19, 22 | mpbid 135 |
. . 3
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24 | 13, 23 | mpd 13 |
. 2
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25 | 1, 24 | syl3an3 1169 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-3an 886 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-v 2553 |
This theorem is referenced by: vtocldf 2599 |
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