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Theorem nfoprab1 5657
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 5619 . 2  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { w  |  E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph ) }
2 nfe1 1428 . . 3  |-  F/ x E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph )
32nfab 2229 . 2  |-  F/_ x { w  |  E. x E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph ) }
41, 3nfcxfr 2222 1  |-  F/_ x { <. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 102    = wceq 1287   E.wex 1424   {cab 2071   F/_wnfc 2212   <.cop 3434   {coprab 5616
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-oprab 5619
This theorem is referenced by:  ssoprab2b  5665  nfmpt21  5674  ovi3  5740  tposoprab  6001
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