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Theorem imai 5354
 Description: Image under the identity relation. Theorem 3.16(viii) of [Monk1] p. 38. (Contributed by NM, 30-Apr-1998.)
Assertion
Ref Expression
imai

Proof of Theorem imai
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dfima3 5345 . 2
2 df-br 4453 . . . . . . . 8
3 vex 3112 . . . . . . . . 9
43ideq 5160 . . . . . . . 8
52, 4bitr3i 251 . . . . . . 7
65anbi2i 694 . . . . . 6
7 ancom 450 . . . . . 6
86, 7bitri 249 . . . . 5
98exbii 1667 . . . 4
10 eleq1 2529 . . . . 5
113, 10ceqsexv 3146 . . . 4
129, 11bitri 249 . . 3
1312abbii 2591 . 2
14 abid2 2597 . 2
151, 13, 143eqtri 2490 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  {cab 2442  <.cop 4035   class class class wbr 4452   cid 4795  "cima 5007 This theorem is referenced by:  rnresi  5355  cnvresid  5663  ecidsn  7379  mbfid  22043 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-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017
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