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Mirrors > Home > ILE Home > Th. List > nfsbv | Unicode version |
Description: If is not free in , it is not free in when is distinct from and . Version of nfsb 1926 requiring more disjoint variables. (Contributed by Wolf Lammen, 7-Feb-2023.) Remove disjoint variable condition on . (Revised by Steven Nguyen, 13-Aug-2023.) Reduce axiom usage. (Revised by Gino Giotto, 25-Aug-2024.) |
Ref | Expression |
---|---|
nfsbv.nf |
Ref | Expression |
---|---|
nfsbv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-sb 1743 | . 2 | |
2 | nfv 1508 | . . . 4 | |
3 | nfsbv.nf | . . . 4 | |
4 | 2, 3 | nfim 1552 | . . 3 |
5 | 2, 3 | nfan 1545 | . . . 4 |
6 | 5 | nfex 1617 | . . 3 |
7 | 4, 6 | nfan 1545 | . 2 |
8 | 1, 7 | nfxfr 1454 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wnf 1440 wex 1472 wsb 1742 |
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-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-4 1490 ax-17 1506 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 |
This theorem is referenced by: sbco2v 1928 cbvabw 2280 |
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