Theorem nfoprab3 6361

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 6312	. 2 |- { <. <. x , y >. , z >. | ph } = { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
2		nfe1 1935	. . . . 5 |- F/ z E. z ( w = <. <. x , y >. , z >. /\ ph )
3	2	nfex 2050	. . . 4 |- F/ z E. y E. z ( w = <. <. x , y >. , z >. /\ ph )
4	3	nfex 2050	. . 3 |- F/ z E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph )
5	4	nfab 2616	. 2 |- F/_ z { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
6	1, 5	nfcxfr 2610	1 |- F/_ z { <. <. x , y >. , z >. | ph }

Syntax hints:   /\ wa 376   = wceq 1452   E.wex 1671   {cab 2457   F/_wnfc 2599   <.cop 3965   {coprab 6309

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451

This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-oprab 6312

This theorem is referenced by:  ssoprab2b  6367  ov3  6452  tposoprab  7027