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Theorem csbima12g 5205
 Description: Move class substitution in and out of the image of a function. (Contributed by FL, 15-Dec-2006.) (Proof shortened by Mario Carneiro, 4-Dec-2016.)
Assertion
Ref Expression
csbima12g

Proof of Theorem csbima12g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq1 3246 . . 3
2 csbeq1 3246 . . . 4
3 csbeq1 3246 . . . 4
42, 3imaeq12d 5196 . . 3
51, 4eqeq12d 2449 . 2
6 vex 2951 . . 3
7 nfcsb1v 3275 . . . 4
8 nfcsb1v 3275 . . . 4
97, 8nfima 5203 . . 3
10 csbeq1a 3251 . . . 4
11 csbeq1a 3251 . . . 4
1210, 11imaeq12d 5196 . . 3
136, 9, 12csbief 3284 . 2
145, 13vtoclg 3003 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  csb 3243  cima 4873 This theorem is referenced by:  csbfv12gALT  5731  disjpreima  24018  csbfv12gALTVD  28938 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 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-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rab 2706  df-v 2950  df-sbc 3154  df-csb 3244  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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