Theorem nfoprab1 6053

Description: The abstraction variables in an operation class abstraction are not free. (Contributed by NM, 25-Apr-1995.) (Revised by David Abernethy, 19-Jun-2012.)

Assertion

Ref	Expression
nfoprab1	|- F/_ x { <. <. x , y >. , z >. | ph }

Proof of Theorem nfoprab1

Dummy variable w is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-oprab 6005	. 2 |- { <. <. x , y >. , z >. | ph } = { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
2		nfe1 1542	. . 3 |- F/ x E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph )
3	2	nfab 2377	. 2 |- F/_ x { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
4	1, 3	nfcxfr 2369	1 |- F/_ x { <. <. x , y >. , z >. | ph }

Syntax hints:   /\ wa 104   = wceq 1395   E.wex 1538   {cab 2215   F/_wnfc 2359   <.cop 3669   {coprab 6002

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-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-oprab 6005

This theorem is referenced by:  ssoprab2b  6061  nfmpo1  6071  ovi3  6142  tposoprab  6426