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Theorem csbriotag 5404
Description: Interchange class substitution and restricted description binder. (Contributed by NM, 24-Feb-2013.)
Assertion
Ref Expression
csbriotag  V  [_  ]_ iota_  iota_  [.  ].
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()    V(,)

Proof of Theorem csbriotag
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq1 2832 . . 3  [_  ]_ iota_  [_  ]_ iota_
2 dfsbcq2 2744 . . . 4  [.  ].
32riotabidv 5395 . . 3  iota_  iota_  [.  ].
41, 3eqeq12d 2036 . 2  [_  ]_ iota_  iota_  [_  ]_ iota_  iota_  [.  ].
5 vex 2538 . . 3 
_V
6 nfs1v 1797 . . . 4  F/
7 nfcv 2160 . . . 4  F/_
86, 7nfriota 5401 . . 3  F/_ iota_
9 sbequ12 1636 . . . 4
109riotabidv 5395 . . 3  iota_  iota_
115, 8, 10csbief 2868 . 2  [_  ]_ iota_  iota_
124, 11vtoclg 2590 1  V  [_  ]_ iota_  iota_  [.  ].
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1228   wcel 1374  wsb 1627   [.wsbc 2741   [_csb 2829   iota_crio 5392
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-3an 875  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-rex 2290  df-v 2537  df-sbc 2742  df-csb 2830  df-sn 3356  df-uni 3555  df-iota 4794  df-riota 5393
This theorem is referenced by: (None)
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