Theorem nfrab1 2645

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 2453	. 2 |- { x e. A | ph } = { x | ( x e. A /\ ph ) }
2		nfab1 2310	. 2 |- F/_ x { x | ( x e. A /\ ph ) }
3	1, 2	nfcxfr 2305	1 |- F/_ x { x e. A | ph }

Syntax hints:   /\ wa 103   e. wcel 2136   {cab 2151   F/_wnfc 2295   {crab 2448

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-11 1494  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-rab 2453

This theorem is referenced by:  repizf2  4141  rabxfrd  4447  onintrab2im  4495  tfis  4560  fvmptssdm  5570  infssuzcldc  11884  nnwosdc  11972  imasnopn  12939