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.

Step	Hyp	Ref	Expression
1		csbiotagOLD 5586	. . 3
2		sbcbrgOLD 4504	. . . . 5
3		csbconstg 3447	. . . . . 6
4	3	breq2d 4464	. . . . 5
5	2, 4	bitrd 253	. . . 4
6	5	iotabidv 5577	. . 3
7	1, 6	eqtrd 2498	. 2
8		df-fv 5601	. . 3
9	8	csbeq2i 3836	. 2
10		df-fv 5601	. 2
11	7, 9, 10	3eqtr4g 2523	1

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