Theorem nfrab1 2677

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 2484	. 2 |- { x e. A | ph } = { x | ( x e. A /\ ph ) }
2		nfab1 2341	. 2 |- F/_ x { x | ( x e. A /\ ph ) }
3	1, 2	nfcxfr 2336	1 |- F/_ x { x e. A | ph }

Syntax hints:   /\ wa 104   e. wcel 2167   {cab 2182   F/_wnfc 2326   {crab 2479

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 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-11 1520  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-rab 2484

This theorem is referenced by:  repizf2  4195  rabxfrd  4504  onintrab2im  4554  tfis  4619  fvmptssdm  5646  infssuzcldc  10325  nnwosdc  12206  imasnopn  14535