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Theorem fnimage 25492
 Description: Image is a function over the set-like portion of . (Contributed by Scott Fenton, 4-Apr-2014.) (Revised by Mario Carneiro, 19-Apr-2014.)
Assertion
Ref Expression
fnimage Image
Distinct variable group:   ,

Proof of Theorem fnimage
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 funimage 25491 . 2 Image
2 vex 2902 . . . . . . . 8
3 vex 2902 . . . . . . . 8
42, 3brimage 25489 . . . . . . 7 Image
5 eleq1 2447 . . . . . . . 8
63, 5mpbii 203 . . . . . . 7
74, 6sylbi 188 . . . . . 6 Image
87exlimiv 1641 . . . . 5 Image
9 eqid 2387 . . . . . . 7
10 brimageg 25490 . . . . . . . 8 Image
112, 10mpan 652 . . . . . . 7 Image
129, 11mpbiri 225 . . . . . 6 Image
13 breq2 4157 . . . . . . 7 Image Image
1413spcegv 2980 . . . . . 6 Image Image
1512, 14mpd 15 . . . . 5 Image
168, 15impbii 181 . . . 4 Image
172eldm 5007 . . . 4 Image Image
18 imaeq2 5139 . . . . . 6
1918eleq1d 2453 . . . . 5
202, 19elab 3025 . . . 4
2116, 17, 203bitr4i 269 . . 3 Image
2221eqriv 2384 . 2 Image
23 df-fn 5397 . 2 Image Image Image
241, 22, 23mpbir2an 887 1 Image
 Colors of variables: wff set class Syntax hints:   wb 177  wex 1547   wceq 1649   wcel 1717  cab 2373  cvv 2899   class class class wbr 4153   cdm 4818  cima 4821   wfun 5388   wfn 5389  Imagecimage 25407 This theorem is referenced by:  imageval  25493 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-13 1719  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368  ax-sep 4271  ax-nul 4279  ax-pow 4318  ax-pr 4344  ax-un 4641 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2242  df-mo 2243  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-ne 2552  df-ral 2654  df-rex 2655  df-rab 2658  df-v 2901  df-sbc 3105  df-dif 3266  df-un 3268  df-in 3270  df-ss 3277  df-nul 3572  df-if 3683  df-sn 3763  df-pr 3764  df-op 3766  df-uni 3958  df-br 4154  df-opab 4208  df-mpt 4209  df-eprel 4435  df-id 4439  df-xp 4824  df-rel 4825  df-cnv 4826  df-co 4827  df-dm 4828  df-rn 4829  df-res 4830  df-ima 4831  df-iota 5358  df-fun 5396  df-fn 5397  df-f 5398  df-fo 5400  df-fv 5402  df-1st 6288  df-2nd 6289  df-symdif 25386  df-txp 25419  df-image 25429
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