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Theorem csbiota 5585
Description: Class substitution within a description binder. (Contributed by Scott Fenton, 6-Oct-2017.) (Revised by NM, 23-Aug-2018.)
Assertion
Ref Expression
csbiota
Distinct variable groups:   ,   ,

Proof of Theorem csbiota
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq1 3437 . . . 4
2 dfsbcq2 3330 . . . . 5
32iotabidv 5577 . . . 4
41, 3eqeq12d 2479 . . 3
5 vex 3112 . . . 4
6 nfs1v 2181 . . . . 5
76nfiota 5560 . . . 4
8 sbequ12 1992 . . . . 5
98iotabidv 5577 . . . 4
105, 7, 9csbief 3459 . . 3
114, 10vtoclg 3167 . 2
12 csbprc 3821 . . 3
13 sbcex 3337 . . . . . 6
1413con3i 135 . . . . 5
1514nexdv 1884 . . . 4
16 euex 2308 . . . . 5
1716con3i 135 . . . 4
18 iotanul 5571 . . . 4
1915, 17, 183syl 20 . . 3
2012, 19eqtr4d 2501 . 2
2111, 20pm2.61i 164 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  =wceq 1395  E.wex 1612  [wsb 1739  e.wcel 1818  E!weu 2282   cvv 3109  [.wsbc 3327  [_csb 3434   c0 3784  iotacio 5554
This theorem is referenced by:  csbfv12  5906
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-fal 1401  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-sn 4030  df-uni 4250  df-iota 5556
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