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Theorem nfoprab1 5872
Description: The abstraction variables in an operation class abstraction are not free. (Contributed by NM, 25-Apr-1995.) (Revised by David Abernethy, 19-Jun-2012.)
Assertion
Ref Expression
nfoprab1  |-  F/_ x { <. <. x ,  y
>. ,  z >.  | 
ph }

Proof of Theorem nfoprab1
Dummy variable  w is distinct from all other variables.
StepHypRef Expression
1 df-oprab 5830 . 2  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { w  |  E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph ) }
2 nfe1 1476 . . 3  |-  F/ x E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph )
32nfab 2304 . 2  |-  F/_ x { w  |  E. x E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph ) }
41, 3nfcxfr 2296 1  |-  F/_ x { <. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 103    = wceq 1335   E.wex 1472   {cab 2143   F/_wnfc 2286   <.cop 3564   {coprab 5827
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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-oprab 5830
This theorem is referenced by:  ssoprab2b  5880  nfmpo1  5890  ovi3  5959  tposoprab  6229
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