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Mirrors > Home > ILE Home > Th. List > nfsn | GIF version |
Description: Bound-variable hypothesis builder for singletons. (Contributed by NM, 14-Nov-1995.) |
Ref | Expression |
---|---|
nfsn.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfsn | ⊢ Ⅎ𝑥{𝐴} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsn2 3536 | . 2 ⊢ {𝐴} = {𝐴, 𝐴} | |
2 | nfsn.1 | . . 3 ⊢ Ⅎ𝑥𝐴 | |
3 | 2, 2 | nfpr 3568 | . 2 ⊢ Ⅎ𝑥{𝐴, 𝐴} |
4 | 1, 3 | nfcxfr 2276 | 1 ⊢ Ⅎ𝑥{𝐴} |
Colors of variables: wff set class |
Syntax hints: Ⅎwnfc 2266 {csn 3522 {cpr 3523 |
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 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 |
This theorem is referenced by: nfop 3716 nfsuc 4325 sniota 5110 dfmpo 6113 |
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