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Theorem dfima3 5345
 Description: Alternate definition of image. Compare definition (d) of [Enderton] p. 44. (Contributed by NM, 14-Aug-1994.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
dfima3
Distinct variable groups:   ,,   ,,

Proof of Theorem dfima3
StepHypRef Expression
1 dfima2 5344 . 2
2 df-br 4453 . . . . 5
32rexbii 2959 . . . 4
4 df-rex 2813 . . . 4
53, 4bitri 249 . . 3
65abbii 2591 . 2
71, 6eqtri 2486 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  {cab 2442  E.wrex 2808  <.cop 4035   class class class wbr 4452  "cima 5007 This theorem is referenced by:  imadmrn  5352  imassrn  5353  imai  5354  funimaexg  5670  cnvimadfsn  6927  rdglim2  7117  dfhe3  37799 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  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-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-xp 5010  df-cnv 5012  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017
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