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Mirrors > Home > ILE Home > Th. List > dfnfc2 | Unicode version |
Description: An alternate 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 2283 | . . . 4 | |
2 | id 19 | . . . 4 | |
3 | 1, 2 | nfeqd 2297 | . . 3 |
4 | 3 | alrimiv 1847 | . 2 |
5 | simpr 109 | . . . . . 6 | |
6 | df-nfc 2271 | . . . . . . 7 | |
7 | velsn 3549 | . . . . . . . . 9 | |
8 | 7 | nfbii 1450 | . . . . . . . 8 |
9 | 8 | albii 1447 | . . . . . . 7 |
10 | 6, 9 | bitri 183 | . . . . . 6 |
11 | 5, 10 | sylibr 133 | . . . . 5 |
12 | 11 | nfunid 3751 | . . . 4 |
13 | nfa1 1522 | . . . . . 6 | |
14 | nfnf1 1524 | . . . . . . 7 | |
15 | 14 | nfal 1556 | . . . . . 6 |
16 | 13, 15 | nfan 1545 | . . . . 5 |
17 | unisng 3761 | . . . . . . 7 | |
18 | 17 | sps 1518 | . . . . . 6 |
19 | 18 | adantr 274 | . . . . 5 |
20 | 16, 19 | nfceqdf 2281 | . . . 4 |
21 | 12, 20 | mpbid 146 | . . 3 |
22 | 21 | ex 114 | . 2 |
23 | 4, 22 | impbid2 142 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1330 wceq 1332 wnf 1437 wcel 1481 wnfc 2269 csn 3532 cuni 3744 |
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-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 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rex 2423 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 df-uni 3745 |
This theorem is referenced by: eusv2nf 4385 |
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