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Theorem nfoprab1 6115
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 6077 . 2  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { w  |  E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph ) }
2 nfe1 1747 . . 3  |-  F/ x E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph )
32nfab 2575 . 2  |-  F/_ x { w  |  E. x E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph ) }
41, 3nfcxfr 2568 1  |-  F/_ x { <. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 359   E.wex 1550    = wceq 1652   {cab 2421   F/_wnfc 2558   <.cop 3809   {coprab 6074
This theorem is referenced by:  ssoprab2b  6123  nfmpt21  6132  ov3  6202  tposoprab  6507
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-oprab 6077
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