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Mirrors > Home > ILE Home > Th. List > Mathboxes > elabgft1 | Unicode version |
Description: One implication of elabgf 2863, in closed form. (Contributed by BJ, 21-Nov-2019.) |
Ref | Expression |
---|---|
elabgf1.nf1 | |
elabgf1.nf2 |
Ref | Expression |
---|---|
elabgft1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biimp 117 | . . . . . 6 | |
2 | imim2 55 | . . . . . 6 | |
3 | 1, 2 | syl5 32 | . . . . 5 |
4 | 3 | imim2i 12 | . . . 4 |
5 | 4 | alimi 1442 | . . 3 |
6 | elabgf1.nf1 | . . . 4 | |
7 | nfab1 2308 | . . . . . 6 | |
8 | 6, 7 | nfel 2315 | . . . . 5 |
9 | elabgf1.nf2 | . . . . 5 | |
10 | 8, 9 | nfim 1559 | . . . 4 |
11 | elabgf0 13499 | . . . 4 | |
12 | 6, 10, 11 | bj-vtoclgft 13497 | . . 3 |
13 | 5, 12 | syl 14 | . 2 |
14 | 13 | pm2.43d 50 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1340 wceq 1342 wnf 1447 wcel 2135 cab 2150 wnfc 2293 |
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-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 |
This theorem is referenced by: elabgf1 13501 |
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