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Theorem dfima2 5197
 Description: Alternate definition of image. Compare definition (d) of [Enderton] p. 44. (Contributed by NM, 19-Apr-2004.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
dfima2
Distinct variable groups:   ,,   ,,

Proof of Theorem dfima2
StepHypRef Expression
1 df-ima 4883 . 2
2 dfrn2 5051 . 2
3 vex 2951 . . . . . . 7
43brres 5144 . . . . . 6
5 ancom 438 . . . . . 6
64, 5bitri 241 . . . . 5
76exbii 1592 . . . 4
8 df-rex 2703 . . . 4
97, 8bitr4i 244 . . 3
109abbii 2547 . 2
111, 2, 103eqtri 2459 1
 Colors of variables: wff set class Syntax hints:   wa 359  wex 1550   wceq 1652   wcel 1725  cab 2421  wrex 2698   class class class wbr 4204   crn 4871   cres 4872  cima 4873 This theorem is referenced by:  dfima3  5198  elimag  5199  imasng  5218  dfimafn  5767  isoini  6050  dffin1-5  8260  dfimafnf  24035  ofpreima  24073  dfaimafn  27996 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 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-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-br 4205  df-opab 4259  df-xp 4876  df-cnv 4878  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883
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