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Theorem csbfv12gOLD 5907
Description: Move class substitution in and out of a function value. (Contributed by NM, 11-Nov-2005.) Obsolete as of 20-Aug-2018. Use csbfv12 5906 instead. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
csbfv12gOLD

Proof of Theorem csbfv12gOLD
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbiotagOLD 5586 . . 3
2 sbcbrgOLD 4504 . . . . 5
3 csbconstg 3447 . . . . . 6
43breq2d 4464 . . . . 5
52, 4bitrd 253 . . . 4
65iotabidv 5577 . . 3
71, 6eqtrd 2498 . 2
8 df-fv 5601 . . 3
98csbeq2i 3836 . 2
10 df-fv 5601 . 2
117, 9, 103eqtr4g 2523 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  [.wsbc 3327  [_csb 3434   class class class wbr 4452  iotacio 5554  `cfv 5593
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  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-iota 5556  df-fv 5601
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