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Theorem csbiota 5582
 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:   ,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem csbiota
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq1 3352 . . . 4
2 dfsbcq2 3258 . . . . 5
32iotabidv 5574 . . . 4
41, 3eqeq12d 2486 . . 3
5 vex 3034 . . . 4
6 nfs1v 2286 . . . . 5
76nfiota 5557 . . . 4
8 sbequ12 2098 . . . . 5
98iotabidv 5574 . . . 4
105, 7, 9csbief 3374 . . 3
114, 10vtoclg 3093 . 2
12 csbprc 3774 . . 3
13 sbcex 3265 . . . . . 6
1413con3i 142 . . . . 5
1514nexdv 1790 . . . 4
16 euex 2343 . . . . 5
1716con3i 142 . . . 4
18 iotanul 5568 . . . 4
1915, 17, 183syl 18 . . 3
2012, 19eqtr4d 2508 . 2
2111, 20pm2.61i 169 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wceq 1452  wex 1671  wsb 1805   wcel 1904  weu 2319  cvv 3031  wsbc 3255  csb 3349  c0 3722  cio 5551 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-fal 1458  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-sbc 3256  df-csb 3350  df-dif 3393  df-in 3397  df-ss 3404  df-nul 3723  df-sn 3960  df-uni 4191  df-iota 5553 This theorem is referenced by:  csbfv12  5914
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