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Theorem brrange 25781
 Description: The binary relationship form of the range 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
brrange Range

Proof of Theorem brrange
StepHypRef Expression
1 brdomain.1 . . 3
2 brdomain.2 . . 3
31, 2brimage 25773 . 2 Image
4 df-range 25714 . . 3 Range Image
54breqi 4220 . 2 Range Image
6 dfrn5 25403 . . 3
76eqeq2i 2448 . 2
83, 5, 73bitr4i 270 1 Range
 Colors of variables: wff set class Syntax hints:   wb 178   wceq 1653   wcel 1726  cvv 2958   class class class wbr 4214   cxp 4878   crn 4881   cres 4882  cima 4883  c2nd 6350  Imagecimage 25686  Rangecrange 25690 This theorem is referenced by:  brrangeg  25783  brrestrict  25796 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pow 4379  ax-pr 4405  ax-un 4703 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-opab 4269  df-mpt 4270  df-eprel 4496  df-id 4500  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-rn 4891  df-res 4892  df-ima 4893  df-iota 5420  df-fun 5458  df-fn 5459  df-f 5460  df-fo 5462  df-fv 5464  df-1st 6351  df-2nd 6352  df-symdif 25665  df-txp 25700  df-image 25710  df-range 25714
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