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Theorem nfoprab3 5587
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 5547 . 2  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { w  |  E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph ) }
2 nfe1 1426 . . . . 5  |-  F/ z E. z ( w  =  <. <. x ,  y
>. ,  z >.  /\ 
ph )
32nfex 1569 . . . 4  |-  F/ z E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph )
43nfex 1569 . . 3  |-  F/ z E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph )
54nfab 2224 . 2  |-  F/_ z { w  |  E. x E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph ) }
61, 5nfcxfr 2217 1  |-  F/_ z { <. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 102    = wceq 1285   E.wex 1422   {cab 2068   F/_wnfc 2207   <.cop 3409   {coprab 5544
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-oprab 5547
This theorem is referenced by:  ssoprab2b  5593  ovi3  5668  tposoprab  5929
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