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Theorem reldom 7905
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 7901 . 2 ≼ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1𝑦}
21relopabi 5205 1 Rel ≼
Colors of variables: wff setvar class
Syntax hints:  wex 1701  Rel wrel 5079  1-1wf1 5844  cdom 7897
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-rab 2916  df-v 3188  df-dif 3558  df-un 3560  df-in 3562  df-ss 3569  df-nul 3892  df-if 4059  df-sn 4149  df-pr 4151  df-op 4155  df-opab 4674  df-xp 5080  df-rel 5081  df-dom 7901
This theorem is referenced by:  relsdom  7906  brdomg  7909  brdomi  7910  domtr  7953  undom  7992  xpdom2  7999  xpdom1g  8001  domunsncan  8004  sbth  8024  sbthcl  8026  dom0  8032  fodomr  8055  pwdom  8056  domssex  8065  mapdom1  8069  mapdom2  8075  fineqv  8119  infsdomnn  8165  infn0  8166  elharval  8412  harword  8414  domwdom  8423  unxpwdom  8438  infdifsn  8498  infdiffi  8499  ac10ct  8801  iunfictbso  8881  cdadom1  8952  cdainf  8958  infcda1  8959  pwcdaidm  8961  cdalepw  8962  unctb  8971  infcdaabs  8972  infunabs  8973  infpss  8983  infmap2  8984  fictb  9011  infpssALT  9079  fin34  9156  ttukeylem1  9275  fodomb  9292  wdomac  9293  brdom3  9294  iundom2g  9306  iundom  9308  infxpidm  9328  iunctb  9340  gchdomtri  9395  pwfseq  9430  pwxpndom2  9431  pwxpndom  9432  pwcdandom  9433  gchpwdom  9436  gchaclem  9444  reexALT  11770  hashdomi  13109  1stcrestlem  21165  2ndcdisj2  21170  dis2ndc  21173  hauspwdom  21214  ufilen  21644  ovoliunnul  23182  uniiccdif  23252  ovoliunnfl  33083  voliunnfl  33085  volsupnfl  33086  nnfoctb  38698  meadjiun  39990  caragenunicl  40045
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