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Mirrors > Home > ILE Home > Th. List > dfnfc2 | Unicode version |
Description: An alternative statement of the effective freeness of a class , when it is a set. (Contributed by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
dfnfc2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcvd 2179 | . . . 4 | |
2 | id 19 | . . . 4 | |
3 | 1, 2 | nfeqd 2192 | . . 3 |
4 | 3 | alrimiv 1754 | . 2 |
5 | simpr 103 | . . . . . 6 | |
6 | df-nfc 2167 | . . . . . . 7 | |
7 | velsn 3392 | . . . . . . . . 9 | |
8 | 7 | nfbii 1362 | . . . . . . . 8 |
9 | 8 | albii 1359 | . . . . . . 7 |
10 | 6, 9 | bitri 173 | . . . . . 6 |
11 | 5, 10 | sylibr 137 | . . . . 5 |
12 | 11 | nfunid 3587 | . . . 4 |
13 | nfa1 1434 | . . . . . 6 | |
14 | nfnf1 1436 | . . . . . . 7 | |
15 | 14 | nfal 1468 | . . . . . 6 |
16 | 13, 15 | nfan 1457 | . . . . 5 |
17 | unisng 3597 | . . . . . . 7 | |
18 | 17 | sps 1430 | . . . . . 6 |
19 | 18 | adantr 261 | . . . . 5 |
20 | 16, 19 | nfceqdf 2177 | . . . 4 |
21 | 12, 20 | mpbid 135 | . . 3 |
22 | 21 | ex 108 | . 2 |
23 | 4, 22 | impbid2 131 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wnf 1349 wcel 1393 wnfc 2165 csn 3375 cuni 3580 |
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-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-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-un 2922 df-sn 3381 df-pr 3382 df-uni 3581 |
This theorem is referenced by: eusv2nf 4188 |
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