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Mirrors > Home > MPE Home > Th. List > vtoclgft | Unicode version |
Description: Closed theorem form of vtoclgf 2978. (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 2932 |
. 2
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2 | elisset 2934 |
. . . . 5
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3 | 2 | 3ad2ant3 980 |
. . . 4
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4 | nfnfc1 2551 |
. . . . . . 7
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5 | nfcvd 2549 |
. . . . . . . 8
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6 | id 20 |
. . . . . . . 8
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7 | 5, 6 | nfeqd 2562 |
. . . . . . 7
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8 | eqeq1 2418 |
. . . . . . . 8
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9 | 8 | a1i 11 |
. . . . . . 7
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10 | 4, 7, 9 | cbvexd 2064 |
. . . . . 6
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11 | 10 | ad2antrr 707 |
. . . . 5
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12 | 11 | 3adant3 977 |
. . . 4
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13 | 3, 12 | mpbid 202 |
. . 3
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14 | bi1 179 |
. . . . . . . . 9
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15 | 14 | imim2i 14 |
. . . . . . . 8
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16 | 15 | com23 74 |
. . . . . . 7
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17 | 16 | imp 419 |
. . . . . 6
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18 | 17 | alanimi 1568 |
. . . . 5
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19 | 18 | 3ad2ant2 979 |
. . . 4
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20 | simp1r 982 |
. . . . 5
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21 | 19.23t 1814 |
. . . . 5
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22 | 20, 21 | syl 16 |
. . . 4
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23 | 19, 22 | mpbid 202 |
. . 3
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24 | 13, 23 | mpd 15 |
. 2
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25 | 1, 24 | syl3an3 1219 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: vtocldf 2971 riotasv2dOLD 6562 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2393 |
This theorem depends on definitions: df-bi 178 df-an 361 df-3an 938 df-ex 1548 df-nf 1551 df-sb 1656 df-clab 2399 df-cleq 2405 df-clel 2408 df-nfc 2537 df-v 2926 |
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