Theorem nfoprab3 6071

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 6021	. 2 |- { <. <. x , y >. , z >. | ph } = { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
2		nfe1 1544	. . . . 5 |- F/ z E. z ( w = <. <. x , y >. , z >. /\ ph )
3	2	nfex 1685	. . . 4 |- F/ z E. y E. z ( w = <. <. x , y >. , z >. /\ ph )
4	3	nfex 1685	. . 3 |- F/ z E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph )
5	4	nfab 2379	. 2 |- F/_ z { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
6	1, 5	nfcxfr 2371	1 |- F/_ z { <. <. x , y >. , z >. | ph }

Syntax hints:   /\ wa 104   = wceq 1397   E.wex 1540   {cab 2217   F/_wnfc 2361   <.cop 3672   {coprab 6018

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-oprab 6021

This theorem is referenced by:  ssoprab2b  6077  ovi3  6158  tposoprab  6445