Theorem reldom 6226

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 6223	. 2 |- ~<_ = { <. x , y >. | E. f f : x -1-1-> y }
2	1	relopabi 4463	1 |- Rel ~<_

Syntax hints:   E.wex 1381   Rel wrel 4350   -1-1->wf1 4899   ~<_ cdom 6220

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944

This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-opab 3819  df-xp 4351  df-rel 4352  df-dom 6223

This theorem is referenced by:  brdomg  6229  brdomi  6230  domtr  6265  xpdom2  6305  xpdom1g  6307