Theorem nfrab1 2726

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 2531	. 2 |- { x e. A | ph } = { x | ( x e. A /\ ph ) }
2		nfab1 2388	. 2 |- F/_ x { x | ( x e. A /\ ph ) }
3	1, 2	nfcxfr 2383	1 |- F/_ x { x e. A | ph }

Syntax hints:   /\ wa 104   e. wcel 2205   {cab 2220   F/_wnfc 2373   {crab 2526

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-rab 2531

This theorem is referenced by:  repizf2  4277  rabxfrd  4592  onintrab2im  4642  tfis  4707  fvmptssdm  5764  infssuzcldc  10599  nnwosdc  12739  imasnopn  15181  lfgrnloopen  16145