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Mirrors > Home > ILE Home > Th. List > nfrexdya | Unicode version |
Description: Not-free for restricted existential quantification where and are distinct. See nfrexdxy 2468 for a version with and distinct instead. (Contributed by Jim Kingdon, 30-May-2018.) |
Ref | Expression |
---|---|
nfraldya.2 | |
nfraldya.3 | |
nfraldya.4 |
Ref | Expression |
---|---|
nfrexdya |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2422 | . 2 | |
2 | sban 1928 | . . . . . 6 | |
3 | clelsb3 2244 | . . . . . . 7 | |
4 | 3 | anbi1i 453 | . . . . . 6 |
5 | 2, 4 | bitri 183 | . . . . 5 |
6 | 5 | exbii 1584 | . . . 4 |
7 | nfv 1508 | . . . . 5 | |
8 | 7 | sb8e 1829 | . . . 4 |
9 | df-rex 2422 | . . . 4 | |
10 | 6, 8, 9 | 3bitr4i 211 | . . 3 |
11 | nfv 1508 | . . . 4 | |
12 | nfraldya.3 | . . . 4 | |
13 | nfraldya.2 | . . . . 5 | |
14 | nfraldya.4 | . . . . 5 | |
15 | 13, 14 | nfsbd 1950 | . . . 4 |
16 | 11, 12, 15 | nfrexdxy 2468 | . . 3 |
17 | 10, 16 | nfxfrd 1451 | . 2 |
18 | 1, 17 | nfxfrd 1451 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wnf 1436 wex 1468 wcel 1480 wsb 1735 wnfc 2268 wrex 2417 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 |
This theorem is referenced by: nfrexya 2474 |
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