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Mirrors > Home > ILE Home > Th. List > Mathboxes > elabgft1 | Unicode version |
Description: One implication of elabgf 2685, in closed form. (Contributed by BJ, 21-Nov-2019.) |
Ref | Expression |
---|---|
elabgf1.nf1 | |
elabgf1.nf2 |
Ref | Expression |
---|---|
elabgft1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi1 111 | . . . . . 6 | |
2 | imim2 49 | . . . . . 6 | |
3 | 1, 2 | syl5 28 | . . . . 5 |
4 | 3 | imim2i 12 | . . . 4 |
5 | 4 | alimi 1344 | . . 3 |
6 | elabgf1.nf1 | . . . 4 | |
7 | nfab1 2180 | . . . . . 6 | |
8 | 6, 7 | nfel 2186 | . . . . 5 |
9 | elabgf1.nf2 | . . . . 5 | |
10 | 8, 9 | nfim 1464 | . . . 4 |
11 | elabgf0 9916 | . . . 4 | |
12 | 6, 10, 11 | bj-vtoclgft 9914 | . . 3 |
13 | 5, 12 | syl 14 | . 2 |
14 | 13 | pm2.43d 44 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wal 1241 wceq 1243 wnf 1349 wcel 1393 cab 2026 wnfc 2165 |
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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 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-tru 1246 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: elabgf1 9918 |
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