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Mirrors > Home > ILE Home > Th. List > vtoclgft | Unicode version |
Description: Closed theorem form of vtoclgf 2739. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
vtoclgft |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2692 | . 2 | |
2 | elisset 2695 | . . . . 5 | |
3 | 2 | 3ad2ant3 1004 | . . . 4 |
4 | nfnfc1 2282 | . . . . . . 7 | |
5 | nfcvd 2280 | . . . . . . . 8 | |
6 | id 19 | . . . . . . . 8 | |
7 | 5, 6 | nfeqd 2294 | . . . . . . 7 |
8 | eqeq1 2144 | . . . . . . . 8 | |
9 | 8 | a1i 9 | . . . . . . 7 |
10 | 4, 7, 9 | cbvexd 1897 | . . . . . 6 |
11 | 10 | ad2antrr 479 | . . . . 5 |
12 | 11 | 3adant3 1001 | . . . 4 |
13 | 3, 12 | mpbid 146 | . . 3 |
14 | bi1 117 | . . . . . . . . 9 | |
15 | 14 | imim2i 12 | . . . . . . . 8 |
16 | 15 | com23 78 | . . . . . . 7 |
17 | 16 | imp 123 | . . . . . 6 |
18 | 17 | alanimi 1435 | . . . . 5 |
19 | 18 | 3ad2ant2 1003 | . . . 4 |
20 | simp1r 1006 | . . . . 5 | |
21 | 19.23t 1655 | . . . . 5 | |
22 | 20, 21 | syl 14 | . . . 4 |
23 | 19, 22 | mpbid 146 | . . 3 |
24 | 13, 23 | mpd 13 | . 2 |
25 | 1, 24 | syl3an3 1251 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 962 wal 1329 wceq 1331 wnf 1436 wex 1468 wcel 1480 wnfc 2266 cvv 2681 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 |
This theorem is referenced by: vtocldf 2732 |
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