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Mirrors > Home > MPE Home > Th. List > vtoclgft | Structured version Visualization version Unicode version |
Description: Closed theorem form of vtoclgf 3264. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 12-Oct-2016.) (Proof shortened by JJ, 11-Aug-2021.) |
Ref | Expression |
---|---|
vtoclgft |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 3215 | . . . . 5 | |
2 | nfnfc1 2767 | . . . . . 6 | |
3 | nfcvd 2765 | . . . . . . 7 | |
4 | id 22 | . . . . . . 7 | |
5 | 3, 4 | nfeqd 2772 | . . . . . 6 |
6 | eqeq1 2626 | . . . . . . 7 | |
7 | 6 | a1i 11 | . . . . . 6 |
8 | 2, 5, 7 | cbvexd 2278 | . . . . 5 |
9 | 1, 8 | syl5ib 234 | . . . 4 |
10 | 9 | ad2antrr 762 | . . 3 |
11 | 10 | 3impia 1261 | . 2 |
12 | biimp 205 | . . . . . . . . 9 | |
13 | 12 | imim2i 16 | . . . . . . . 8 |
14 | 13 | com23 86 | . . . . . . 7 |
15 | 14 | imp 445 | . . . . . 6 |
16 | 15 | alanimi 1744 | . . . . 5 |
17 | 19.23t 2079 | . . . . . 6 | |
18 | 17 | adantl 482 | . . . . 5 |
19 | 16, 18 | syl5ib 234 | . . . 4 |
20 | 19 | imp 445 | . . 3 |
21 | 20 | 3adant3 1081 | . 2 |
22 | 11, 21 | mpd 15 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wal 1481 wceq 1483 wex 1704 wnf 1708 wcel 1990 wnfc 2751 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 |
This theorem is referenced by: vtocldf 3256 bj-vtoclgfALT 33021 |
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