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Theorem csbfv12 5906
 Description: Move class substitution in and out of a function value. (Contributed by NM, 11-Nov-2005.) (Revised by NM, 20-Aug-2018.)
Assertion
Ref Expression
csbfv12

Proof of Theorem csbfv12
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbiota 5585 . . . 4
2 sbcbr123 4503 . . . . . 6
3 csbconstg 3447 . . . . . . 7
43breq2d 4464 . . . . . 6
52, 4syl5bb 257 . . . . 5
65iotabidv 5577 . . . 4
71, 6syl5eq 2510 . . 3
8 df-fv 5601 . . . 4
98csbeq2i 3836 . . 3
10 df-fv 5601 . . 3
117, 9, 103eqtr4g 2523 . 2
12 csbprc 3821 . . 3
13 csbprc 3821 . . . . 5
1413fveq1d 5873 . . . 4
15 0fv 5904 . . . 4
1614, 15syl6req 2515 . . 3
1712, 16eqtrd 2498 . 2
1811, 17pm2.61i 164 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  =wceq 1395  e.wcel 1818   cvv 3109  [.wsbc 3327  [_csb 3434   c0 3784   class class class wbr 4452  iotacio 5554  `cfv 5593 This theorem is referenced by:  csbfv2g  5908  coe1fzgsumdlem  18343  evl1gsumdlem  18392  cdlemk42  36667 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-nul 4581  ax-pow 4630 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-fal 1401  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-dm 5014  df-iota 5556  df-fv 5601
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