Theorem nfrab1 2674

Description: The abstraction variable in a restricted class abstraction isn't free. (Contributed by NM, 19-Mar-1997.)

Assertion

Ref	Expression
nfrab1	|- F/_ x { x e. A | ph }

Proof of Theorem nfrab1

Step	Hyp	Ref	Expression
1		df-rab 2481	. 2 |- { x e. A | ph } = { x | ( x e. A /\ ph ) }
2		nfab1 2338	. 2 |- F/_ x { x | ( x e. A /\ ph ) }
3	1, 2	nfcxfr 2333	1 |- F/_ x { x e. A | ph }

Syntax hints:   /\ wa 104   e. wcel 2164   {cab 2179   F/_wnfc 2323   {crab 2476

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-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-rab 2481

This theorem is referenced by:  repizf2  4191  rabxfrd  4500  onintrab2im  4550  tfis  4615  fvmptssdm  5642  infssuzcldc  12088  nnwosdc  12176  imasnopn  14467