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Mirrors > Home > ILE Home > Th. List > vtoclgft | Unicode version |
Description: Closed theorem form of vtoclgf 2657. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
vtoclgft |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2610 | . 2 | |
2 | elisset 2613 | . . . . 5 | |
3 | 2 | 3ad2ant3 961 | . . . 4 |
4 | nfnfc1 2222 | . . . . . . 7 | |
5 | nfcvd 2220 | . . . . . . . 8 | |
6 | id 19 | . . . . . . . 8 | |
7 | 5, 6 | nfeqd 2233 | . . . . . . 7 |
8 | eqeq1 2087 | . . . . . . . 8 | |
9 | 8 | a1i 9 | . . . . . . 7 |
10 | 4, 7, 9 | cbvexd 1843 | . . . . . 6 |
11 | 10 | ad2antrr 471 | . . . . 5 |
12 | 11 | 3adant3 958 | . . . 4 |
13 | 3, 12 | mpbid 145 | . . 3 |
14 | bi1 116 | . . . . . . . . 9 | |
15 | 14 | imim2i 12 | . . . . . . . 8 |
16 | 15 | com23 77 | . . . . . . 7 |
17 | 16 | imp 122 | . . . . . 6 |
18 | 17 | alanimi 1388 | . . . . 5 |
19 | 18 | 3ad2ant2 960 | . . . 4 |
20 | simp1r 963 | . . . . 5 | |
21 | 19.23t 1607 | . . . . 5 | |
22 | 20, 21 | syl 14 | . . . 4 |
23 | 19, 22 | mpbid 145 | . . 3 |
24 | 13, 23 | mpd 13 | . 2 |
25 | 1, 24 | syl3an3 1204 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 w3a 919 wal 1282 wceq 1284 wnf 1389 wex 1421 wcel 1433 wnfc 2206 cvv 2601 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 |
This theorem is referenced by: vtocldf 2650 |
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