Theorem nfrab1 2732

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 2537	. 2 |- { x e. A | ph } = { x | ( x e. A /\ ph ) }
2		nfab1 2394	. 2 |- F/_ x { x | ( x e. A /\ ph ) }
3	1, 2	nfcxfr 2389	1 |- F/_ x { x e. A | ph }

This proof depends on syntax axioms:   /\ wa 104   e. wcel 2209   {cab 2224   F/_wnfc 2379   {crab 2532

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-rab 2537

This theorem is used by:  repizf2  4299  rabxfrd  4615  onintrab2im  4665  tfis  4730  fvmptssdm  5790  infssuzcldc  10668  nnwosdc  12816  ballotfilem7  13279  ballotfilemth  13281  imasnopn  15400  lfgrnloopen  16374