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Theorem nfoprab2 5789
Description: The abstraction variables in an operation class abstraction are not free. (Contributed by NM, 25-Apr-1995.) (Revised by David Abernethy, 30-Jul-2012.)
Assertion
Ref Expression
nfoprab2  |-  F/_ y { <. <. x ,  y
>. ,  z >.  | 
ph }

Proof of Theorem nfoprab2
Dummy variable  w is distinct from all other variables.
StepHypRef Expression
1 df-oprab 5746 . 2  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { w  |  E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph ) }
2 nfe1 1457 . . . 4  |-  F/ y E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph )
32nfex 1601 . . 3  |-  F/ y E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph )
43nfab 2263 . 2  |-  F/_ y { w  |  E. x E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph ) }
51, 4nfcxfr 2255 1  |-  F/_ y { <. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 103    = wceq 1316   E.wex 1453   {cab 2103   F/_wnfc 2245   <.cop 3500   {coprab 5743
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-oprab 5746
This theorem is referenced by:  ssoprab2b  5796  nfmpo2  5807  ovi3  5875  tposoprab  6145
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