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Theorem brdom 7520
 Description: Dominance relation. (Contributed by NM, 15-Jun-1998.)
Hypothesis
Ref Expression
bren.1
Assertion
Ref Expression
brdom
Distinct variable groups:   ,   ,

Proof of Theorem brdom
StepHypRef Expression
1 bren.1 . 2
2 brdomg 7518 . 2
31, 2ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:   wb 184  wex 1591   wcel 1762  cvv 3108   class class class wbr 4442  wf1 5578   cdom 7506 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-8 1764  ax-9 1766  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1963  ax-ext 2440  ax-sep 4563  ax-nul 4571  ax-pr 4681  ax-un 6569 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 970  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-eu 2274  df-mo 2275  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2612  df-ne 2659  df-ral 2814  df-rex 2815  df-rab 2818  df-v 3110  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3781  df-if 3935  df-sn 4023  df-pr 4025  df-op 4029  df-uni 4241  df-br 4443  df-opab 4501  df-xp 5000  df-rel 5001  df-cnv 5002  df-dm 5004  df-rn 5005  df-fn 5584  df-f 5585  df-f1 5586  df-dom 7510 This theorem is referenced by:  domen  7521  domtr  7560  sbthlem10  7628  1sdom  7714  ac10ct  8406  domtriomlem  8813  2ndcdisj  19718  birthdaylem3  23006
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