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Theorem brwdomi 8015
Description: Property of weak dominance, forward direction only. (Contributed by Mario Carneiro, 5-May-2015.)
Assertion
Ref Expression
brwdomi
Distinct variable groups:   ,   ,

Proof of Theorem brwdomi
StepHypRef Expression
1 relwdom 8013 . . . 4
21brrelex2i 5046 . . 3
3 brwdom 8014 . . 3
42, 3syl 16 . 2
54ibi 241 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  \/wo 368  =wceq 1395  E.wex 1612  e.wcel 1818   cvv 3109   c0 3784   class class class wbr 4452  -onto->wfo 5591   cwdom 8004
This theorem is referenced by:  numwdom  8461
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691  ax-un 6592
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-cnv 5012  df-dm 5014  df-rn 5015  df-fn 5596  df-fo 5599  df-wdom 8006
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