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Mirrors > Home > ILE Home > Th. List > nfsbcd | Unicode version |
Description: Deduction version of nfsbc 2966. (Contributed by NM, 23-Nov-2005.) (Revised by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
nfsbcd.1 | |
nfsbcd.2 | |
nfsbcd.3 |
Ref | Expression |
---|---|
nfsbcd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-sbc 2947 | . 2 | |
2 | nfsbcd.2 | . . 3 | |
3 | nfsbcd.1 | . . . 4 | |
4 | nfsbcd.3 | . . . 4 | |
5 | 3, 4 | nfabd 2326 | . . 3 |
6 | 2, 5 | nfeld 2322 | . 2 |
7 | 1, 6 | nfxfrd 1462 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wnf 1447 wcel 2135 cab 2150 wnfc 2293 wsbc 2946 |
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 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-sbc 2947 |
This theorem is referenced by: nfsbc 2966 nfcsbd 3075 sbcnestgf 3091 |
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