Theorem nfsn 3765

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

Hypothesis

Ref	Expression
nfsn.1	|- F/_ x A

Assertion

Ref	Expression
nfsn	|- F/_ x { A }

Proof of Theorem nfsn

Step	Hyp	Ref	Expression
1		dfsn2 3719	. 2 |- { A } = { A , A }
2		nfsn.1	. . 3 |- F/_ x A
3	2, 2	nfpr 3755	. 2 |- F/_ x { A , A }
4	1, 3	nfcxfr 2389	1 |- F/_ x { A }

Syntax hints:   F/_wnfc 2379   {csn 3705   {cpr 3706

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-v 2823  df-un 3224  df-sn 3711  df-pr 3712

This theorem is referenced by:  nfop  3915  nfsuc  4548  sniota  5363  dfmpo  6449