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Mirrors > Home > ILE Home > Th. List > nfsbxyt | Unicode version |
Description: Closed form of nfsbxy 1915. (Contributed by Jim Kingdon, 9-May-2018.) |
Ref | Expression |
---|---|
nfsbxyt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-bndl 1486 | . 2 | |
2 | nfs1v 1912 | . . . . 5 | |
3 | drsb1 1771 | . . . . . 6 | |
4 | 3 | drnf2 1712 | . . . . 5 |
5 | 2, 4 | mpbii 147 | . . . 4 |
6 | 5 | a1d 22 | . . 3 |
7 | a16nf 1838 | . . . . 5 | |
8 | 7 | a1d 22 | . . . 4 |
9 | df-nf 1437 | . . . . . 6 | |
10 | 9 | albii 1446 | . . . . 5 |
11 | sb5 1859 | . . . . . . 7 | |
12 | nfa1 1521 | . . . . . . . . 9 | |
13 | nfa1 1521 | . . . . . . . . 9 | |
14 | 12, 13 | nfan 1544 | . . . . . . . 8 |
15 | sp 1488 | . . . . . . . . . 10 | |
16 | 15 | adantr 274 | . . . . . . . . 9 |
17 | sp 1488 | . . . . . . . . . 10 | |
18 | 17 | adantl 275 | . . . . . . . . 9 |
19 | 16, 18 | nfand 1547 | . . . . . . . 8 |
20 | 14, 19 | nfexd 1734 | . . . . . . 7 |
21 | 11, 20 | nfxfrd 1451 | . . . . . 6 |
22 | 21 | ex 114 | . . . . 5 |
23 | 10, 22 | sylbir 134 | . . . 4 |
24 | 8, 23 | jaoi 705 | . . 3 |
25 | 6, 24 | jaoi 705 | . 2 |
26 | 1, 25 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wo 697 wal 1329 wnf 1436 wex 1468 wsb 1735 |
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 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 |
This theorem is referenced by: nfsbt 1949 |
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