MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  csbriota Unicode version

Theorem csbriota 6269
Description: Interchange class substitution and restricted description binder. (Contributed by NM, 24-Feb-2013.) (Revised by NM, 2-Sep-2018.)
Assertion
Ref Expression
csbriota
Distinct variable groups:   ,   ,   ,

Proof of Theorem csbriota
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq1 3437 . . . 4
2 dfsbcq2 3330 . . . . 5
32riotabidv 6259 . . . 4
41, 3eqeq12d 2479 . . 3
5 vex 3112 . . . 4
6 nfs1v 2181 . . . . 5
7 nfcv 2619 . . . . 5
86, 7nfriota 6266 . . . 4
9 sbequ12 1992 . . . . 5
109riotabidv 6259 . . . 4
115, 8, 10csbief 3459 . . 3
124, 11vtoclg 3167 . 2
13 csbprc 3821 . . 3
14 df-riota 6257 . . . 4
15 euex 2308 . . . . . . 7
16 sbcex 3337 . . . . . . . . 9
1716adantl 466 . . . . . . . 8
1817exlimiv 1722 . . . . . . 7
1915, 18syl 16 . . . . . 6
2019con3i 135 . . . . 5
21 iotanul 5571 . . . . 5
2220, 21syl 16 . . . 4
2314, 22syl5req 2511 . . 3
2413, 23eqtrd 2498 . 2
2512, 24pm2.61i 164 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  /\wa 369  =wceq 1395  E.wex 1612  [wsb 1739  e.wcel 1818  E!weu 2282   cvv 3109  [.wsbc 3327  [_csb 3434   c0 3784  iotacio 5554  iota_crio 6256
This theorem is referenced by:  csbriotagOLD  6270  cdlemkid3N  36659  cdlemkid4  36660
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  df-riota 6257
  Copyright terms: Public domain W3C validator