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Theorem nfoprab3 5901
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 5854 . 2  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { w  |  E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph ) }
2 nfe1 1489 . . . . 5  |-  F/ z E. z ( w  =  <. <. x ,  y
>. ,  z >.  /\ 
ph )
32nfex 1630 . . . 4  |-  F/ z E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph )
43nfex 1630 . . 3  |-  F/ z E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph )
54nfab 2317 . 2  |-  F/_ z { w  |  E. x E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph ) }
61, 5nfcxfr 2309 1  |-  F/_ z { <. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 103    = wceq 1348   E.wex 1485   {cab 2156   F/_wnfc 2299   <.cop 3584   {coprab 5851
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-oprab 5854
This theorem is referenced by:  ssoprab2b  5907  ovi3  5986  tposoprab  6256
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