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Mirrors > Home > NFE 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 3747 | . 2 ⊢ {A} = {A, A} | |
2 | nfsn.1 | . . 3 ⊢ ℲxA | |
3 | 2, 2 | nfpr 3773 | . 2 ⊢ Ⅎx{A, A} |
4 | 1, 3 | nfcxfr 2486 | 1 ⊢ Ⅎx{A} |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2476 {csn 3737 {cpr 3738 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-un 3214 df-sn 3741 df-pr 3742 |
This theorem is referenced by: nfopk 4068 sniota 4369 |
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