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Theorem fnimage 25766
 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 25765 . 2 Image
2 vex 2951 . . . . . . . 8
3 vex 2951 . . . . . . . 8
42, 3brimage 25763 . . . . . . 7 Image
5 eleq1 2495 . . . . . . . 8
63, 5mpbii 203 . . . . . . 7
74, 6sylbi 188 . . . . . 6 Image
87exlimiv 1644 . . . . 5 Image
9 eqid 2435 . . . . . . 7
10 brimageg 25764 . . . . . . . 8 Image
112, 10mpan 652 . . . . . . 7 Image
129, 11mpbiri 225 . . . . . 6 Image
13 breq2 4208 . . . . . . 7 Image Image
1413spcegv 3029 . . . . . 6 Image Image
1512, 14mpd 15 . . . . 5 Image
168, 15impbii 181 . . . 4 Image
172eldm 5059 . . . 4 Image Image
18 imaeq2 5191 . . . . . 6
1918eleq1d 2501 . . . . 5
202, 19elab 3074 . . . 4
2116, 17, 203bitr4i 269 . . 3 Image
2221eqriv 2432 . 2 Image
23 df-fn 5449 . 2 Image Image Image
241, 22, 23mpbir2an 887 1 Image
 Colors of variables: wff set class Syntax hints:   wb 177  wex 1550   wceq 1652   wcel 1725  cab 2421  cvv 2948   class class class wbr 4204   cdm 4870  cima 4873   wfun 5440   wfn 5441  Imagecimage 25676 This theorem is referenced by:  imageval  25767 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pow 4369  ax-pr 4395  ax-un 4693 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-mpt 4260  df-eprel 4486  df-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-iota 5410  df-fun 5448  df-fn 5449  df-f 5450  df-fo 5452  df-fv 5454  df-1st 6341  df-2nd 6342  df-symdif 25655  df-txp 25690  df-image 25700
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