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Mirrors > Home > ILE Home > Th. List > dvelimdf | Unicode version |
Description: Deduction form of dvelimf 1991. This version may be useful if we want to avoid ax-17 1507 and use ax-16 1787 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 1503 | . . 3 |
4 | nfsb4t 1990 | . . 3 | |
5 | 3, 4 | syl 14 | . 2 |
6 | dvelimdf.1 | . . 3 | |
7 | dvelimdf.4 | . . . 4 | |
8 | dvelimdf.5 | . . . 4 | |
9 | 1, 7, 8 | sbied 1762 | . . 3 |
10 | 6, 9 | nfbidf 1520 | . 2 |
11 | 5, 10 | sylibd 148 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wal 1330 wnf 1437 wsb 1736 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 |
This theorem is referenced by: dvelimdc 2302 |
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