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Theorem nfoprab2 6294
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 6248 . 2  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { w  |  E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph ) }
2 nfe1 1894 . . . 4  |-  F/ y E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph )
32nfex 2008 . . 3  |-  F/ y E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph )
43nfab 2568 . 2  |-  F/_ y { w  |  E. x E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph ) }
51, 4nfcxfr 2562 1  |-  F/_ y { <. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff setvar class
Syntax hints:    /\ wa 370    = wceq 1437   E.wex 1657   {cab 2409   F/_wnfc 2551   <.cop 3942   {coprab 6245
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2058  ax-ext 2403
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2410  df-cleq 2416  df-clel 2419  df-nfc 2553  df-oprab 6248
This theorem is referenced by:  ssoprab2b  6301  nfmpt22  6312  ov3  6386  tposoprab  6959
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