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Theorem compss 8804
 Description: Express image under of the complementation isomorphism. (Contributed by Stefan O'Rear, 5-Nov-2014.) (Proof shortened by Mario Carneiro, 17-May-2015.)
Hypothesis
Ref Expression
compss.a
Assertion
Ref Expression
compss
Distinct variable groups:   ,,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem compss
StepHypRef Expression
1 compss.a . . . 4
21compsscnv 8799 . . 3
32imaeq1i 5185 . 2
4 difeq2 3583 . . . . 5
54cbvmptv 4518 . . . 4
61, 5eqtri 2458 . . 3
76mptpreima 5348 . 2
83, 7eqtr3i 2460 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1437   wcel 1870  crab 2786   cdif 3439  cpw 3985   cmpt 4484  ccnv 4853  cima 4857 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-9 1874  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407  ax-sep 4548  ax-nul 4556  ax-pr 4661 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-eu 2270  df-mo 2271  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ne 2627  df-ral 2787  df-rex 2788  df-rab 2791  df-v 3089  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-pw 3987  df-sn 4003  df-pr 4005  df-op 4009  df-br 4427  df-opab 4485  df-mpt 4486  df-xp 4860  df-rel 4861  df-cnv 4862  df-dm 4864  df-rn 4865  df-res 4866  df-ima 4867 This theorem is referenced by:  isf34lem4  8805
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