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Theorem reldom 7921
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 7917 . 2 ≼ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1𝑦}
21relopabi 5215 1 Rel ≼
Colors of variables: wff setvar class
Syntax hints:  wex 1701  Rel wrel 5089  1-1wf1 5854  cdom 7913
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 2917  df-v 3192  df-dif 3563  df-un 3565  df-in 3567  df-ss 3574  df-nul 3898  df-if 4065  df-sn 4156  df-pr 4158  df-op 4162  df-opab 4684  df-xp 5090  df-rel 5091  df-dom 7917
This theorem is referenced by:  relsdom  7922  brdomg  7925  brdomi  7926  domtr  7969  undom  8008  xpdom2  8015  xpdom1g  8017  domunsncan  8020  sbth  8040  sbthcl  8042  dom0  8048  fodomr  8071  pwdom  8072  domssex  8081  mapdom1  8085  mapdom2  8091  fineqv  8135  infsdomnn  8181  infn0  8182  elharval  8428  harword  8430  domwdom  8439  unxpwdom  8454  infdifsn  8514  infdiffi  8515  ac10ct  8817  iunfictbso  8897  cdadom1  8968  cdainf  8974  infcda1  8975  pwcdaidm  8977  cdalepw  8978  unctb  8987  infcdaabs  8988  infunabs  8989  infpss  8999  infmap2  9000  fictb  9027  infpssALT  9095  fin34  9172  ttukeylem1  9291  fodomb  9308  wdomac  9309  brdom3  9310  iundom2g  9322  iundom  9324  infxpidm  9344  iunctb  9356  gchdomtri  9411  pwfseq  9446  pwxpndom2  9447  pwxpndom  9448  pwcdandom  9449  gchpwdom  9452  gchaclem  9460  reexALT  11786  hashdomi  13125  1stcrestlem  21195  2ndcdisj2  21200  dis2ndc  21203  hauspwdom  21244  ufilen  21674  ovoliunnul  23215  uniiccdif  23286  ovoliunnfl  33122  voliunnfl  33124  volsupnfl  33125  nnfoctb  38735  meadjiun  40020  caragenunicl  40075
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