Theorem nfsn 3784

Description: Bound-variable hypothesis builder for singletons. (Contributed by NM, 14-Nov-1995.)

Hypothesis

Ref	Expression
nfsn.1	⊢ ℲxA

Assertion

Ref	Expression
nfsn	⊢ Ⅎx{A}

Proof of Theorem nfsn

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}

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