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Theorem reloprab 5584
Description: An operation class abstraction is a relation. (Contributed by NM, 16-Jun-2004.)
Assertion
Ref Expression
reloprab  |-  Rel  { <. <. x ,  y
>. ,  z >.  | 
ph }
Distinct variable groups:    x, z    y,
z
Allowed substitution hints:    ph( x, y, z)

Proof of Theorem reloprab
Dummy variable  w is distinct from all other variables.
StepHypRef Expression
1 dfoprab2 5583 . 2  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { <. w ,  z >.  |  E. x E. y ( w  =  <. x ,  y
>.  /\  ph ) }
21relopabi 4491 1  |-  Rel  { <. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 102    = wceq 1285   E.wex 1422   <.cop 3409   Rel wrel 4376   {coprab 5544
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-opab 3848  df-xp 4377  df-rel 4378  df-oprab 5547
This theorem is referenced by:  oprabss  5621
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