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Theorem reloprab 5901
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 5900 . 2  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { <. w ,  z >.  |  E. x E. y ( w  =  <. x ,  y
>.  /\  ph ) }
21relopabi 4737 1  |-  Rel  { <. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 103    = wceq 1348   E.wex 1485   <.cop 3586   Rel wrel 4616   {coprab 5854
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-14 2144  ax-ext 2152  ax-sep 4107  ax-pow 4160  ax-pr 4194
This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-ral 2453  df-rex 2454  df-v 2732  df-un 3125  df-in 3127  df-ss 3134  df-pw 3568  df-sn 3589  df-pr 3590  df-op 3592  df-opab 4051  df-xp 4617  df-rel 4618  df-oprab 5857
This theorem is referenced by:  oprabss  5939
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