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Mirrors > Home > ILE Home > Th. List > vtoclgft | Unicode version |
Description: Closed theorem form of vtoclgf 2612. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
vtoclgft |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2566 | . 2 | |
2 | elisset 2568 | . . . . 5 | |
3 | 2 | 3ad2ant3 927 | . . . 4 |
4 | nfnfc1 2181 | . . . . . . 7 | |
5 | nfcvd 2179 | . . . . . . . 8 | |
6 | id 19 | . . . . . . . 8 | |
7 | 5, 6 | nfeqd 2192 | . . . . . . 7 |
8 | eqeq1 2046 | . . . . . . . 8 | |
9 | 8 | a1i 9 | . . . . . . 7 |
10 | 4, 7, 9 | cbvexd 1802 | . . . . . 6 |
11 | 10 | ad2antrr 457 | . . . . 5 |
12 | 11 | 3adant3 924 | . . . 4 |
13 | 3, 12 | mpbid 135 | . . 3 |
14 | bi1 111 | . . . . . . . . 9 | |
15 | 14 | imim2i 12 | . . . . . . . 8 |
16 | 15 | com23 72 | . . . . . . 7 |
17 | 16 | imp 115 | . . . . . 6 |
18 | 17 | alanimi 1348 | . . . . 5 |
19 | 18 | 3ad2ant2 926 | . . . 4 |
20 | simp1r 929 | . . . . 5 | |
21 | 19.23t 1567 | . . . . 5 | |
22 | 20, 21 | syl 14 | . . . 4 |
23 | 19, 22 | mpbid 135 | . . 3 |
24 | 13, 23 | mpd 13 | . 2 |
25 | 1, 24 | syl3an3 1170 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 w3a 885 wal 1241 wceq 1243 wnf 1349 wex 1381 wcel 1393 wnfc 2165 cvv 2557 |
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 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 |
This theorem is referenced by: vtocldf 2605 |
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