Theorem nfoprab1 5585

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 5547	. 2 |- { <. <. x , y >. , z >. | ph } = { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
2		nfe1 1426	. . 3 |- F/ x E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph )
3	2	nfab 2224	. 2 |- F/_ x { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
4	1, 3	nfcxfr 2217	1 |- F/_ x { <. <. x , y >. , z >. | ph }

Syntax hints:   /\ wa 102   = wceq 1285   E.wex 1422   {cab 2068   F/_wnfc 2207   <.cop 3409   {coprab 5544

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-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064

This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-oprab 5547

This theorem is referenced by:  ssoprab2b  5593  nfmpt21  5602  ovi3  5668  tposoprab  5929