Theorem nfoprab3 6357

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 6310	. 2 |- { <. <. x , y >. , z >. | ph } = { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
2		nfe1 1894	. . . . 5 |- F/ z E. z ( w = <. <. x , y >. , z >. /\ ph )
3	2	nfex 2008	. . . 4 |- F/ z E. y E. z ( w = <. <. x , y >. , z >. /\ ph )
4	3	nfex 2008	. . 3 |- F/ z E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph )
5	4	nfab 2584	. 2 |- F/_ z { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
6	1, 5	nfcxfr 2578	1 |- F/_ z { <. <. x , y >. , z >. | ph }

Syntax hints:   /\ wa 370   = wceq 1437   E.wex 1657   {cab 2407   F/_wnfc 2566   <.cop 4004   {coprab 6307

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401

This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-oprab 6310

This theorem is referenced by:  ssoprab2b  6363  ov3  6448  tposoprab  7021