Theorem reldom 6892

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 6889	. 2 |- ~<_ = { <. x , y >. | E. f f : x -1-1-> y }
2	1	relopabi 4847	1 |- Rel ~<_

Syntax hints:   E.wex 1538   Rel wrel 4724   -1-1->wf1 5315   ~<_ cdom 6886

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-14 2203  ax-ext 2211  ax-sep 4202  ax-pow 4258  ax-pr 4293

This theorem depends on definitions:  df-bi 117  df-3an 1004  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-ral 2513  df-rex 2514  df-v 2801  df-un 3201  df-in 3203  df-ss 3210  df-pw 3651  df-sn 3672  df-pr 3673  df-op 3675  df-opab 4146  df-xp 4725  df-rel 4726  df-dom 6889

This theorem is referenced by:  brdomg  6897  brdomi  6898  ctex  6902  domssr  6929  domtr  6937  xpdom2  6990  xpdom1g  6992  mapdom1g  7008  isbth  7134  djudom  7260  difinfsn  7267  hashinfom  11000