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Theorem nfoprab3 6128
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.
StepHypRef Expression
1 df-oprab 6088 . 2  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { w  |  E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph ) }
2 nfe1 1748 . . . . 5  |-  F/ z E. z ( w  =  <. <. x ,  y
>. ,  z >.  /\ 
ph )
32nfex 1866 . . . 4  |-  F/ z E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph )
43nfex 1866 . . 3  |-  F/ z E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph )
54nfab 2578 . 2  |-  F/_ z { w  |  E. x E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph ) }
61, 5nfcxfr 2571 1  |-  F/_ z { <. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 360   E.wex 1551    = wceq 1653   {cab 2424   F/_wnfc 2561   <.cop 3819   {coprab 6085
This theorem is referenced by:  ssoprab2b  6134  ov3  6213  tposoprab  6518
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-oprab 6088
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