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Mirrors > Home > ILE Home > Th. List > nfsbxy | Unicode version |
Description: Similar to hbsb 1864 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 1439 | . 2 | |
2 | nfs1v 1856 | . . . 4 | |
3 | drsb1 1720 | . . . . 5 | |
4 | 3 | drnf2 1662 | . . . 4 |
5 | 2, 4 | mpbii 146 | . . 3 |
6 | a16nf 1787 | . . . 4 | |
7 | df-nf 1390 | . . . . . 6 | |
8 | 7 | albii 1399 | . . . . 5 |
9 | sb5 1808 | . . . . . 6 | |
10 | nfa1 1474 | . . . . . . 7 | |
11 | sp 1441 | . . . . . . . 8 | |
12 | nfsbxy.1 | . . . . . . . . 9 | |
13 | 12 | a1i 9 | . . . . . . . 8 |
14 | 11, 13 | nfand 1500 | . . . . . . 7 |
15 | 10, 14 | nfexd 1684 | . . . . . 6 |
16 | 9, 15 | nfxfrd 1404 | . . . . 5 |
17 | 8, 16 | sylbir 133 | . . . 4 |
18 | 6, 17 | jaoi 668 | . . 3 |
19 | 5, 18 | jaoi 668 | . 2 |
20 | 1, 19 | ax-mp 7 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wo 661 wal 1282 wnf 1389 wex 1421 wsb 1685 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 |
This theorem is referenced by: nfsb 1863 sbalyz 1916 opelopabsb 4015 bezoutlemmain 10387 |
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