Theorem nfoprab3 6129

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 6079	. 2 |- { <. <. x , y >. , z >. | ph } = { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
2		nfe1 1549	. . . . 5 |- F/ z E. z ( w = <. <. x , y >. , z >. /\ ph )
3	2	nfex 1690	. . . 4 |- F/ z E. y E. z ( w = <. <. x , y >. , z >. /\ ph )
4	3	nfex 1690	. . 3 |- F/ z E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph )
5	4	nfab 2397	. 2 |- F/_ z { w | E. x E. y E. z ( w = <. <. x , y >. , z >. /\ ph ) }
6	1, 5	nfcxfr 2389	1 |- F/_ z { <. <. x , y >. , z >. | ph }

Syntax hints:   /\ wa 104   = wceq 1402   E.wex 1545   {cab 2224   F/_wnfc 2379   <.cop 3708   {coprab 6076

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 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-oprab 6079

This theorem is referenced by:  ssoprab2b  6135  ovi3  6216  tposoprab  6541