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Mirrors > Home > ILE Home > Th. List > dvelimdc | Unicode version |
Description: Deduction form of dvelimc 2198. (Contributed by Mario Carneiro, 8-Oct-2016.) |
Ref | Expression |
---|---|
dvelimdc.1 | |
dvelimdc.2 | |
dvelimdc.3 | |
dvelimdc.4 | |
dvelimdc.5 |
Ref | Expression |
---|---|
dvelimdc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1421 | . . 3 | |
2 | dvelimdc.1 | . . . . 5 | |
3 | dvelimdc.2 | . . . . 5 | |
4 | dvelimdc.3 | . . . . . 6 | |
5 | 4 | nfcrd 2191 | . . . . 5 |
6 | dvelimdc.4 | . . . . . 6 | |
7 | 6 | nfcrd 2191 | . . . . 5 |
8 | dvelimdc.5 | . . . . . 6 | |
9 | eleq2 2101 | . . . . . 6 | |
10 | 8, 9 | syl6 29 | . . . . 5 |
11 | 2, 3, 5, 7, 10 | dvelimdf 1892 | . . . 4 |
12 | 11 | imp 115 | . . 3 |
13 | 1, 12 | nfcd 2173 | . 2 |
14 | 13 | ex 108 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wb 98 wal 1241 wceq 1243 wnf 1349 wcel 1393 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-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 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 df-cleq 2033 df-clel 2036 df-nfc 2167 |
This theorem is referenced by: dvelimc 2198 |
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