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Theorem nfoprab2 6320
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 6274 . 2  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { w  |  E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph ) }
2 nfe1 1845 . . . 4  |-  F/ y E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph )
32nfex 1953 . . 3  |-  F/ y E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph )
43nfab 2620 . 2  |-  F/_ y { w  |  E. x E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph ) }
51, 4nfcxfr 2614 1  |-  F/_ y { <. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff setvar class
Syntax hints:    /\ wa 367    = wceq 1398   E.wex 1617   {cab 2439   F/_wnfc 2602   <.cop 4022   {coprab 6271
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-oprab 6274
This theorem is referenced by:  ssoprab2b  6327  nfmpt22  6338  ov3  6412  tposoprab  6983
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