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Theorem cbviin 3723
 Description: Change bound variables in an indexed intersection. (Contributed by Jeff Hankins, 26-Aug-2009.) (Revised by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
cbviun.1
cbviun.2
cbviun.3
Assertion
Ref Expression
cbviin
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbviin
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbviun.1 . . . . 5
21nfcri 2188 . . . 4
3 cbviun.2 . . . . 5
43nfcri 2188 . . . 4
5 cbviun.3 . . . . 5
65eleq2d 2123 . . . 4
72, 4, 6cbvral 2546 . . 3
87abbii 2169 . 2
9 df-iin 3688 . 2
10 df-iin 3688 . 2
118, 9, 103eqtr4i 2086 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1259   wcel 1409  cab 2042  wnfc 2181  wral 2323  ciin 3686 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-iin 3688 This theorem is referenced by:  cbviinv  3725
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