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Mirrors > Home > ILE Home > Th. List > dvelimdf | Unicode version |
Description: Deduction form of dvelimf 1891. This version may be useful if we want to avoid ax-17 1419 and use ax-16 1695 instead. (Contributed by NM, 7-Apr-2004.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 11-May-2018.) |
Ref | Expression |
---|---|
dvelimdf.1 | |
dvelimdf.2 | |
dvelimdf.3 | |
dvelimdf.4 | |
dvelimdf.5 |
Ref | Expression |
---|---|
dvelimdf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dvelimdf.2 | . . . 4 | |
2 | dvelimdf.3 | . . . 4 | |
3 | 1, 2 | alrimi 1415 | . . 3 |
4 | nfsb4t 1890 | . . 3 | |
5 | 3, 4 | syl 14 | . 2 |
6 | dvelimdf.1 | . . 3 | |
7 | dvelimdf.4 | . . . 4 | |
8 | dvelimdf.5 | . . . 4 | |
9 | 1, 7, 8 | sbied 1671 | . . 3 |
10 | 6, 9 | nfbidf 1432 | . 2 |
11 | 5, 10 | sylibd 138 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 98 wal 1241 wnf 1349 wsb 1645 |
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-in1 544 ax-in2 545 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 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 |
This theorem is referenced by: dvelimdc 2197 |
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