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Theorem reldom 7107
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 7103 . 2  |-  ~<_  =  { <. x ,  y >.  |  E. f  f : x -1-1-> y }
21relopabi 4992 1  |-  Rel  ~<_
Colors of variables: wff set class
Syntax hints:   E.wex 1550   Rel wrel 4875   -1-1->wf1 5443    ~<_ cdom 7099
This theorem is referenced by:  relsdom  7108  brdomg  7110  brdomi  7111  domtr  7152  undom  7188  xpdom2  7195  xpdom1g  7197  domunsncan  7200  sbth  7219  sbthcl  7221  dom0  7227  fodomr  7250  pwdom  7251  domssex  7260  mapdom1  7264  mapdom2  7270  fineqv  7316  infsdomnn  7360  infn0  7361  elharval  7523  harword  7525  domwdom  7534  unxpwdom  7549  infdifsn  7603  infdiffi  7604  ac10ct  7907  iunfictbso  7987  cdadom1  8058  cdainf  8064  infcda1  8065  pwcdaidm  8067  cdalepw  8068  unctb  8077  infcdaabs  8078  infunabs  8079  infpss  8089  infmap2  8090  fictb  8117  infpssALT  8185  fin34  8262  ttukeylem1  8381  fodomb  8396  wdomac  8397  brdom3  8398  iundom2g  8407  iundom  8409  infxpidm  8429  iunctb  8441  gchdomtri  8496  pwfseq  8531  pwxpndom2  8532  pwxpndom  8533  pwcdandom  8534  gchaclem  8537  gchpwdom  8541  reexALT  10598  hashdomi  11646  cctop  17062  1stcrestlem  17507  2ndcdisj2  17512  dis2ndc  17515  hauspwdom  17556  ufilen  17954  ovoliunnul  19395  uniiccdif  19462  ovoliunnfl  26238  voliunnfl  26240  volsupnfl  26241
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-opab 4259  df-xp 4876  df-rel 4877  df-dom 7103
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