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Mirrors > Home > ILE Home > Th. List > Mathboxes > elabgft1 | Unicode version |
Description: One implication of elabgf 2736, in closed form. (Contributed by BJ, 21-Nov-2019.) |
Ref | Expression |
---|---|
elabgf1.nf1 | |
elabgf1.nf2 |
Ref | Expression |
---|---|
elabgft1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi1 116 | . . . . . 6 | |
2 | imim2 54 | . . . . . 6 | |
3 | 1, 2 | syl5 32 | . . . . 5 |
4 | 3 | imim2i 12 | . . . 4 |
5 | 4 | alimi 1384 | . . 3 |
6 | elabgf1.nf1 | . . . 4 | |
7 | nfab1 2221 | . . . . . 6 | |
8 | 6, 7 | nfel 2227 | . . . . 5 |
9 | elabgf1.nf2 | . . . . 5 | |
10 | 8, 9 | nfim 1504 | . . . 4 |
11 | elabgf0 10587 | . . . 4 | |
12 | 6, 10, 11 | bj-vtoclgft 10585 | . . 3 |
13 | 5, 12 | syl 14 | . 2 |
14 | 13 | pm2.43d 49 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wal 1282 wceq 1284 wnf 1389 wcel 1433 cab 2067 wnfc 2206 |
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-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 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-tru 1287 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: elabgf1 10589 |
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