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Theorem nfoprab2 5898
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 5862 . 2  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { w  |  E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph ) }
2 nfe1 1706 . . . 4  |-  F/ y E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph )
32nfex 1767 . . 3  |-  F/ y E. x E. y E. z ( w  = 
<. <. x ,  y
>. ,  z >.  /\ 
ph )
43nfab 2423 . 2  |-  F/_ y { w  |  E. x E. y E. z
( w  =  <. <.
x ,  y >. ,  z >.  /\  ph ) }
51, 4nfcxfr 2416 1  |-  F/_ y { <. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 358   E.wex 1528    = wceq 1623   {cab 2269   F/_wnfc 2406   <.cop 3643   {coprab 5859
This theorem is referenced by:  ssoprab2b  5905  nfmpt22  5915  ov3  5984  tposoprab  6270
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-oprab 5862
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