Theorem nfrab1 2657

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 2464	. 2 |- { x e. A | ph } = { x | ( x e. A /\ ph ) }
2		nfab1 2321	. 2 |- F/_ x { x | ( x e. A /\ ph ) }
3	1, 2	nfcxfr 2316	1 |- F/_ x { x e. A | ph }

Syntax hints:   /\ wa 104   e. wcel 2148   {cab 2163   F/_wnfc 2306   {crab 2459

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rab 2464

This theorem is referenced by:  repizf2  4164  rabxfrd  4471  onintrab2im  4519  tfis  4584  fvmptssdm  5602  infssuzcldc  11954  nnwosdc  12042  imasnopn  13884