Theorem nfrab1 2538

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 2362	. 2 |- { x e. A | ph } = { x | ( x e. A /\ ph ) }
2		nfab1 2225	. 2 |- F/_ x { x | ( x e. A /\ ph ) }
3	1, 2	nfcxfr 2220	1 |- F/_ x { x e. A | ph }

Syntax hints:   /\ wa 102   e. wcel 1434   {cab 2069   F/_wnfc 2210   {crab 2357

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-ext 2065

This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-rab 2362

This theorem is referenced by:  repizf2  3956  rabxfrd  4247  onintrab2im  4290  tfis  4352  fvmptssdm  5308  infssuzcldc  10572