ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  reloprab Unicode version

Theorem reloprab 5872
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 5871 . 2  |-  { <. <.
x ,  y >. ,  z >.  |  ph }  =  { <. w ,  z >.  |  E. x E. y ( w  =  <. x ,  y
>.  /\  ph ) }
21relopabi 4715 1  |-  Rel  { <. <. x ,  y
>. ,  z >.  | 
ph }
Colors of variables: wff set class
Syntax hints:    /\ wa 103    = wceq 1335   E.wex 1472   <.cop 3564   Rel wrel 4594   {coprab 5828
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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-14 2131  ax-ext 2139  ax-sep 4085  ax-pow 4138  ax-pr 4172
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-rex 2441  df-v 2714  df-un 3106  df-in 3108  df-ss 3115  df-pw 3546  df-sn 3567  df-pr 3568  df-op 3570  df-opab 4029  df-xp 4595  df-rel 4596  df-oprab 5831
This theorem is referenced by:  oprabss  5910
  Copyright terms: Public domain W3C validator