Theorem nfrab1 2610

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 2425	. 2 |- { x e. A | ph } = { x | ( x e. A /\ ph ) }
2		nfab1 2283	. 2 |- F/_ x { x | ( x e. A /\ ph ) }
3	1, 2	nfcxfr 2278	1 |- F/_ x { x e. A | ph }

Syntax hints:   /\ wa 103   e. wcel 1480   {cab 2125   F/_wnfc 2268   {crab 2420

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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rab 2425

This theorem is referenced by:  repizf2  4086  rabxfrd  4390  onintrab2im  4434  tfis  4497  fvmptssdm  5505  infssuzcldc  11644  imasnopn  12468