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Mirrors > Home > ILE Home > Th. List > dvelimdc | Unicode version |
Description: Deduction form of dvelimc 2279. (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 1493 | . . 3 | |
2 | dvelimdc.1 | . . . . 5 | |
3 | dvelimdc.2 | . . . . 5 | |
4 | dvelimdc.3 | . . . . . 6 | |
5 | 4 | nfcrd 2272 | . . . . 5 |
6 | dvelimdc.4 | . . . . . 6 | |
7 | 6 | nfcrd 2272 | . . . . 5 |
8 | dvelimdc.5 | . . . . . 6 | |
9 | eleq2 2181 | . . . . . 6 | |
10 | 8, 9 | syl6 33 | . . . . 5 |
11 | 2, 3, 5, 7, 10 | dvelimdf 1969 | . . . 4 |
12 | 11 | imp 123 | . . 3 |
13 | 1, 12 | nfcd 2253 | . 2 |
14 | 13 | ex 114 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wal 1314 wceq 1316 wnf 1421 wcel 1465 wnfc 2245 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-cleq 2110 df-clel 2113 df-nfc 2247 |
This theorem is referenced by: dvelimc 2279 |
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