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Theorem reldom 7418
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 7414 . 2  |-  ~<_  =  { <. x ,  y >.  |  E. f  f : x -1-1-> y }
21relopabi 5065 1  |-  Rel  ~<_
Colors of variables: wff setvar class
Syntax hints:   E.wex 1587   Rel wrel 4945   -1-1->wf1 5515    ~<_ cdom 7410
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430  ax-sep 4513  ax-nul 4521  ax-pr 4631
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ne 2646  df-ral 2800  df-rex 2801  df-rab 2804  df-v 3072  df-dif 3431  df-un 3433  df-in 3435  df-ss 3442  df-nul 3738  df-if 3892  df-sn 3978  df-pr 3980  df-op 3984  df-opab 4451  df-xp 4946  df-rel 4947  df-dom 7414
This theorem is referenced by:  relsdom  7419  brdomg  7422  brdomi  7423  domtr  7464  undom  7501  xpdom2  7508  xpdom1g  7510  domunsncan  7513  sbth  7533  sbthcl  7535  dom0  7541  fodomr  7564  pwdom  7565  domssex  7574  mapdom1  7578  mapdom2  7584  fineqv  7631  infsdomnn  7676  infn0  7677  elharval  7881  harword  7883  domwdom  7892  unxpwdom  7907  infdifsn  7965  infdiffi  7966  ac10ct  8307  iunfictbso  8387  cdadom1  8458  cdainf  8464  infcda1  8465  pwcdaidm  8467  cdalepw  8468  unctb  8477  infcdaabs  8478  infunabs  8479  infpss  8489  infmap2  8490  fictb  8517  infpssALT  8585  fin34  8662  ttukeylem1  8781  fodomb  8796  wdomac  8797  brdom3  8798  iundom2g  8807  iundom  8809  infxpidm  8829  iunctb  8841  gchdomtri  8899  pwfseq  8934  pwxpndom2  8935  pwxpndom  8936  pwcdandom  8937  gchpwdom  8940  gchaclem  8948  reexALT  11088  hashdomi  12247  cctop  18728  1stcrestlem  19174  2ndcdisj2  19179  dis2ndc  19182  hauspwdom  19223  ufilen  19621  ovoliunnul  21108  uniiccdif  21176  ovoliunnfl  28573  voliunnfl  28575  volsupnfl  28576
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