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Mirrors > Home > ILE Home > Th. List > nfsbxyt | Unicode version |
Description: Closed form of nfsbxy 1929. (Contributed by Jim Kingdon, 9-May-2018.) |
Ref | Expression |
---|---|
nfsbxyt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-bndl 1496 | . 2 | |
2 | nfs1v 1926 | . . . . 5 | |
3 | drsb1 1786 | . . . . . 6 | |
4 | 3 | drnf2 1721 | . . . . 5 |
5 | 2, 4 | mpbii 147 | . . . 4 |
6 | 5 | a1d 22 | . . 3 |
7 | a16nf 1853 | . . . . 5 | |
8 | 7 | a1d 22 | . . . 4 |
9 | df-nf 1448 | . . . . . 6 | |
10 | 9 | albii 1457 | . . . . 5 |
11 | sb5 1874 | . . . . . . 7 | |
12 | nfa1 1528 | . . . . . . . . 9 | |
13 | nfa1 1528 | . . . . . . . . 9 | |
14 | 12, 13 | nfan 1552 | . . . . . . . 8 |
15 | sp 1498 | . . . . . . . . . 10 | |
16 | 15 | adantr 274 | . . . . . . . . 9 |
17 | sp 1498 | . . . . . . . . . 10 | |
18 | 17 | adantl 275 | . . . . . . . . 9 |
19 | 16, 18 | nfand 1555 | . . . . . . . 8 |
20 | 14, 19 | nfexd 1748 | . . . . . . 7 |
21 | 11, 20 | nfxfrd 1462 | . . . . . 6 |
22 | 21 | ex 114 | . . . . 5 |
23 | 10, 22 | sylbir 134 | . . . 4 |
24 | 8, 23 | jaoi 706 | . . 3 |
25 | 6, 24 | jaoi 706 | . 2 |
26 | 1, 25 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wo 698 wal 1340 wnf 1447 wex 1479 wsb 1749 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 |
This theorem is referenced by: nfsbt 1963 |
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