Theorem reldom 8518

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.

Step	Hyp	Ref	Expression
1		df-dom 8514	. 2 ⊢ ≼ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥–1-1→𝑦}
2	1	relopabi 5697	1 ⊢ Rel ≼

Syntax hints:  ∃wex 1779  Rel wrel 5563  –1-1→wf1 6355   ≼ cdom 8510

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-10 2144  ax-11 2160  ax-12 2176  ax-ext 2796

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1539  df-ex 1780  df-nf 1784  df-sb 2069  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2966  df-rab 3150  df-v 3499  df-dif 3942  df-un 3944  df-in 3946  df-ss 3955  df-nul 4295  df-if 4471  df-sn 4571  df-pr 4573  df-op 4577  df-opab 5132  df-xp 5564  df-rel 5565  df-dom 8514

This theorem is referenced by:  relsdom  8519  brdomg  8522  brdomi  8523  ctex  8527  domtr  8565  undom  8608  xpdom2  8615  xpdom1g  8617  domunsncan  8620  sbth  8640  sbthcl  8642  dom0  8648  fodomr  8671  pwdom  8672  domssex  8681  mapdom1  8685  mapdom2  8691  fineqv  8736  infsdomnn  8782  infn0  8783  elharval  9030  harword  9032  domwdom  9041  unxpwdom  9056  infdifsn  9123  infdiffi  9124  ac10ct  9463  djudom2  9612  djuinf  9617  infdju1  9618  pwdjuidm  9620  djulepw  9621  infdjuabs  9631  infunabs  9632  pwdjudom  9641  infpss  9642  infmap2  9643  fictb  9670  infpssALT  9738  fin34  9815  ttukeylem1  9934  fodomb  9951  wdomac  9952  brdom3  9953  iundom2g  9965  iundom  9967  infxpidm  9987  gchdomtri  10054  pwfseq  10089  pwxpndom2  10090  pwxpndom  10091  pwdjundom  10092  gchdjuidm  10093  gchpwdom  10095  gchaclem  10103  reexALT  12386  hashdomi  13744  1stcrestlem  22063  hauspwdom  22112  ufilen  22541  ovoliunnul  24111  ovoliunnfl  34938  voliunnfl  34940  volsupnfl  34941  nnfoctb  41315  meadjiun  42755  caragenunicl  42813