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Theorem csbima12g 4900
 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 3006 . . 3
2 csbeq1 3006 . . . 4
3 csbeq1 3006 . . . 4
42, 3imaeq12d 4882 . . 3
51, 4eqeq12d 2154 . 2
6 vex 2689 . . 3
7 nfcsb1v 3035 . . . 4
8 nfcsb1v 3035 . . . 4
97, 8nfima 4889 . . 3
10 csbeq1a 3012 . . . 4
11 csbeq1a 3012 . . . 4
1210, 11imaeq12d 4882 . . 3
136, 9, 12csbief 3044 . 2
145, 13vtoclg 2746 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1331   wcel 1480  csb 3003  cima 4542 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rab 2425  df-v 2688  df-sbc 2910  df-csb 3004  df-un 3075  df-in 3077  df-ss 3084  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930  df-opab 3990  df-xp 4545  df-cnv 4547  df-dm 4549  df-rn 4550  df-res 4551  df-ima 4552 This theorem is referenced by: (None)
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