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Mirrors > Home > ILE Home > Th. List > nfraldya | Unicode version |
Description: Not-free for restricted universal quantification where and are distinct. See nfraldxy 2508 for a version with and distinct instead. (Contributed by Jim Kingdon, 30-May-2018.) |
Ref | Expression |
---|---|
nfraldya.2 | |
nfraldya.3 | |
nfraldya.4 |
Ref | Expression |
---|---|
nfraldya |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2458 | . 2 | |
2 | sbim 1951 | . . . . . 6 | |
3 | clelsb1 2280 | . . . . . . 7 | |
4 | 3 | imbi1i 238 | . . . . . 6 |
5 | 2, 4 | bitri 184 | . . . . 5 |
6 | 5 | albii 1468 | . . . 4 |
7 | nfv 1526 | . . . . 5 | |
8 | 7 | sb8 1854 | . . . 4 |
9 | df-ral 2458 | . . . 4 | |
10 | 6, 8, 9 | 3bitr4i 212 | . . 3 |
11 | nfv 1526 | . . . 4 | |
12 | nfraldya.3 | . . . 4 | |
13 | nfraldya.2 | . . . . 5 | |
14 | nfraldya.4 | . . . . 5 | |
15 | 13, 14 | nfsbd 1975 | . . . 4 |
16 | 11, 12, 15 | nfraldxy 2508 | . . 3 |
17 | 10, 16 | nfxfrd 1473 | . 2 |
18 | 1, 17 | nfxfrd 1473 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1351 wnf 1458 wsb 1760 wcel 2146 wnfc 2304 wral 2453 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1445 ax-7 1446 ax-gen 1447 ax-ie1 1491 ax-ie2 1492 ax-8 1502 ax-10 1503 ax-11 1504 ax-i12 1505 ax-bndl 1507 ax-4 1508 ax-17 1524 ax-i9 1528 ax-ial 1532 ax-i5r 1533 ax-ext 2157 |
This theorem depends on definitions: df-bi 117 df-nf 1459 df-sb 1761 df-cleq 2168 df-clel 2171 df-nfc 2306 df-ral 2458 |
This theorem is referenced by: nfralya 2515 |
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