Theorem nfoprab3 5904

Description: The abstraction variables in an operation class abstraction are not free. (Contributed by NM, 22-Aug-2013.)

Assertion

Ref	Expression
nfoprab3	|- F/_ z { <. <. x , y >. , z >. | ph }

Proof of Theorem nfoprab3

Dummy variable w is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-oprab 5857	. 2 |- { <. <. x , y >. , z >. | ph } = { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
2		nfe1 1489	. . . . 5 |- F/ z E. z ( w = <. <. x , y >. , z >. /\ ph )
3	2	nfex 1630	. . . 4 |- F/ z E. y E. z ( w = <. <. x , y >. , z >. /\ ph )
4	3	nfex 1630	. . 3 |- F/ z E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph )
5	4	nfab 2317	. 2 |- F/_ z { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
6	1, 5	nfcxfr 2309	1 |- F/_ z { <. <. x , y >. , z >. | ph }

Syntax hints:   /\ wa 103   = wceq 1348   E.wex 1485   {cab 2156   F/_wnfc 2299   <.cop 3586   {coprab 5854

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-oprab 5857

This theorem is referenced by:  ssoprab2b  5910  ovi3  5989  tposoprab  6259