Theorem reldom 7524

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 7520	. 2 |- ~<_ = { <. x , y >. | E. f f : x -1-1-> y }
2	1	relopabi 5118	1 |- Rel ~<_

Syntax hints:   E.wex 1599   Rel wrel 4994   -1-1->wf1 5575   ~<_ cdom 7516

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-9 1808  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421  ax-sep 4558  ax-nul 4566  ax-pr 4676

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-ral 2798  df-rex 2799  df-rab 2802  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021  df-opab 4496  df-xp 4995  df-rel 4996  df-dom 7520

This theorem is referenced by:  relsdom  7525  brdomg  7528  brdomi  7529  domtr  7570  undom  7607  xpdom2  7614  xpdom1g  7616  domunsncan  7619  sbth  7639  sbthcl  7641  dom0  7647  fodomr  7670  pwdom  7671  domssex  7680  mapdom1  7684  mapdom2  7690  fineqv  7737  infsdomnn  7783  infn0  7784  elharval  7992  harword  7994  domwdom  8003  unxpwdom  8018  infdifsn  8076  infdiffi  8077  ac10ct  8418  iunfictbso  8498  cdadom1  8569  cdainf  8575  infcda1  8576  pwcdaidm  8578  cdalepw  8579  unctb  8588  infcdaabs  8589  infunabs  8590  infpss  8600  infmap2  8601  fictb  8628  infpssALT  8696  fin34  8773  ttukeylem1  8892  fodomb  8907  wdomac  8908  brdom3  8909  iundom2g  8918  iundom  8920  infxpidm  8940  iunctb  8952  gchdomtri  9010  pwfseq  9045  pwxpndom2  9046  pwxpndom  9047  pwcdandom  9048  gchpwdom  9051  gchaclem  9059  reexALT  11223  hashdomi  12427  cctop  19380  1stcrestlem  19826  2ndcdisj2  19831  dis2ndc  19834  hauspwdom  19875  ufilen  20304  ovoliunnul  21791  uniiccdif  21860  ovoliunnfl  30031  voliunnfl  30033  volsupnfl  30034