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Theorem nfoprab1 6062
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 6024 . 2  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { w  |  E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph ) }
2 nfe1 1739 . . 3  |-  F/ x E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph )
32nfab 2527 . 2  |-  F/_ x { w  |  E. x E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph ) }
41, 3nfcxfr 2520 1  |-  F/_ x { <. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 359   E.wex 1547    = wceq 1649   {cab 2373   F/_wnfc 2510   <.cop 3760   {coprab 6021
This theorem is referenced by:  ssoprab2b  6070  nfmpt21  6079  ov3  6149  tposoprab  6451
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-oprab 6024
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