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Theorem imai 5210
 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 5198 . 2
2 df-br 4205 . . . . . . . 8
3 vex 2951 . . . . . . . . 9
43ideq 5017 . . . . . . . 8
52, 4bitr3i 243 . . . . . . 7
65anbi2i 676 . . . . . 6
7 ancom 438 . . . . . 6
86, 7bitri 241 . . . . 5
98exbii 1592 . . . 4
10 eleq1 2495 . . . . 5
113, 10ceqsexv 2983 . . . 4
129, 11bitri 241 . . 3
1312abbii 2547 . 2
14 abid2 2552 . 2
151, 13, 143eqtri 2459 1
 Colors of variables: wff set class Syntax hints:   wa 359  wex 1550   wceq 1652   wcel 1725  cab 2421  cop 3809   class class class wbr 4204   cid 4485  cima 4873 This theorem is referenced by:  rnresi  5211  cnvresid  5515  ecidsn  6945  mbfid  19520 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-id 4490  df-xp 4876  df-rel 4877  df-cnv 4878  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883
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