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Theorem nfoprab3 6092
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 6052 . 2  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { w  |  E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph ) }
2 nfe1 1743 . . . . 5  |-  F/ z E. z ( w  =  <. <. x ,  y
>. ,  z >.  /\ 
ph )
32nfex 1861 . . . 4  |-  F/ z E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph )
43nfex 1861 . . 3  |-  F/ z E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph )
54nfab 2552 . 2  |-  F/_ z { w  |  E. x E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph ) }
61, 5nfcxfr 2545 1  |-  F/_ z { <. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 359   E.wex 1547    = wceq 1649   {cab 2398   F/_wnfc 2535   <.cop 3785   {coprab 6049
This theorem is referenced by:  ssoprab2b  6098  ov3  6177  tposoprab  6482
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-oprab 6052
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