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Theorem csbafv12g 28000
 Description: Move class substitution in and out of a function value, analogous to csbfv12g 5535, with a direct proof proposed by Mario Carneiro, analogous to csbovg 5889. (Contributed by Alexander van der Vekens, 23-Jul-2017.)
Assertion
Ref Expression
csbafv12g ''' '''

Proof of Theorem csbafv12g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq1 3084 . . 3 ''' '''
2 csbeq1 3084 . . . 4
3 csbeq1 3084 . . . 4
42, 3afveq12d 27996 . . 3 ''' '''
51, 4eqeq12d 2297 . 2 ''' ''' ''' '''
6 vex 2791 . . 3
7 nfcsb1v 3113 . . . 4
8 nfcsb1v 3113 . . . 4
97, 8nfafv 27999 . . 3 '''
10 csbeq1a 3089 . . . 4
11 csbeq1a 3089 . . . 4
1210, 11afveq12d 27996 . . 3 ''' '''
136, 9, 12csbief 3122 . 2 ''' '''
145, 13vtoclg 2843 1 ''' '''
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1623   wcel 1684  csb 3081  '''cafv 27972 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pow 4188  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-csb 3082  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702  df-iota 5219  df-fun 5257  df-fv 5263  df-dfat 27974  df-afv 27975
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