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Mirrors > Home > ILE Home > Th. List > nfsbxy | Unicode version |
Description: Similar to hbsb 1922 but with an extra distinct variable constraint, on and . (Contributed by Jim Kingdon, 19-Mar-2018.) |
Ref | Expression |
---|---|
nfsbxy.1 |
Ref | Expression |
---|---|
nfsbxy |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-bndl 1486 | . 2 | |
2 | nfs1v 1912 | . . . 4 | |
3 | drsb1 1771 | . . . . 5 | |
4 | 3 | drnf2 1712 | . . . 4 |
5 | 2, 4 | mpbii 147 | . . 3 |
6 | a16nf 1838 | . . . 4 | |
7 | df-nf 1437 | . . . . . 6 | |
8 | 7 | albii 1446 | . . . . 5 |
9 | sb5 1859 | . . . . . 6 | |
10 | nfa1 1521 | . . . . . . 7 | |
11 | sp 1488 | . . . . . . . 8 | |
12 | nfsbxy.1 | . . . . . . . . 9 | |
13 | 12 | a1i 9 | . . . . . . . 8 |
14 | 11, 13 | nfand 1547 | . . . . . . 7 |
15 | 10, 14 | nfexd 1734 | . . . . . 6 |
16 | 9, 15 | nfxfrd 1451 | . . . . 5 |
17 | 8, 16 | sylbir 134 | . . . 4 |
18 | 6, 17 | jaoi 705 | . . 3 |
19 | 5, 18 | jaoi 705 | . 2 |
20 | 1, 19 | 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: nfsb 1919 sbalyz 1974 opelopabsb 4182 bezoutlemmain 11686 |
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