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Theorem nfoprab1 6355
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 6310 . 2  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { w  |  E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph ) }
2 nfe1 1894 . . 3  |-  F/ x E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph )
32nfab 2584 . 2  |-  F/_ x { w  |  E. x E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph ) }
41, 3nfcxfr 2578 1  |-  F/_ x { <. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff setvar class
Syntax hints:    /\ wa 370    = wceq 1437   E.wex 1657   {cab 2407   F/_wnfc 2566   <.cop 4004   {coprab 6307
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 2057  ax-ext 2401
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 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-oprab 6310
This theorem is referenced by:  ssoprab2b  6363  nfmpt21  6373  ov3  6448  tposoprab  7021
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