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Theorem domintreflemb 25165
 Description: In a reflexive class , an element belongs to the field iff the pair belongs to . (Contributed by FL, 30-Dec-2011.)
Assertion
Ref Expression
domintreflemb
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem domintreflemb
StepHypRef Expression
1 id 19 . . . . 5
21, 1breq12d 4052 . . . 4
32rspccv 2894 . . 3
43adantl 452 . 2
5 breldmg 4900 . . . . 5
653expia 1153 . . . 4
76anidms 626 . . 3
87adantr 451 . 2
94, 8impbid 183 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358   wceq 1632   wcel 1696  wral 2556   class class class wbr 4039   cdm 4705 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-dm 4715
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