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Theorem brdomain 29788
 Description: The binary relationship form of the domain function. (Contributed by Scott Fenton, 11-Apr-2014.) (Revised by Mario Carneiro, 19-Apr-2014.)
Hypotheses
Ref Expression
brdomain.1
brdomain.2
Assertion
Ref Expression
brdomain Domain

Proof of Theorem brdomain
StepHypRef Expression
1 brdomain.1 . . 3
2 brdomain.2 . . 3
31, 2brimage 29781 . 2 Image
4 df-domain 29721 . . 3 Domain Image
54breqi 4462 . 2 Domain Image
6 dfdm5 29423 . . 3
76eqeq2i 2475 . 2
83, 5, 73bitr4i 277 1 Domain
 Colors of variables: wff setvar class Syntax hints:   wb 184   wceq 1395   wcel 1819  cvv 3109   class class class wbr 4456   cxp 5006   cdm 5008   cres 5010  cima 5011  c1st 6797  Imagecimage 29694  Domaincdomain 29697 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-8 1821  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-sep 4578  ax-nul 4586  ax-pow 4634  ax-pr 4695  ax-un 6591 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-eu 2287  df-mo 2288  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-sbc 3328  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-symdif 3725  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-uni 4252  df-br 4457  df-opab 4516  df-mpt 4517  df-eprel 4800  df-id 4804  df-xp 5014  df-rel 5015  df-cnv 5016  df-co 5017  df-dm 5018  df-rn 5019  df-res 5020  df-ima 5021  df-iota 5557  df-fun 5596  df-fn 5597  df-f 5598  df-fo 5600  df-fv 5602  df-1st 6799  df-2nd 6800  df-txp 29708  df-image 29718  df-domain 29721 This theorem is referenced by:  brdomaing  29790  dfrdg4  29805  tfrqfree  29806
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