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Theorem reldom 6314
Description: Dominance is a relation. (Contributed by NM, 28-Mar-1998.)
Assertion
Ref Expression
reldom  |-  Rel  ~<_

Proof of Theorem reldom
Dummy variables  x  y  f are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-dom 6311 . 2  |-  ~<_  =  { <. x ,  y >.  |  E. f  f : x -1-1-> y }
21relopabi 4511 1  |-  Rel  ~<_
Colors of variables: wff set class
Syntax hints:   E.wex 1422   Rel wrel 4396   -1-1->wf1 4949    ~<_ cdom 6308
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 2065  ax-sep 3916  ax-pow 3968  ax-pr 3992
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-v 2612  df-un 2986  df-in 2988  df-ss 2995  df-pw 3402  df-sn 3422  df-pr 3423  df-op 3425  df-opab 3860  df-xp 4397  df-rel 4398  df-dom 6311
This theorem is referenced by:  brdomg  6317  brdomi  6318  domtr  6354  xpdom2  6397  xpdom1g  6399  hashinfom  9872
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