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Theorem cbviin 4307
 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 2606 . . . 4
3 cbviun.2 . . . . 5
43nfcri 2606 . . . 4
5 cbviun.3 . . . . 5
65eleq2d 2534 . . . 4
72, 4, 6cbvral 3001 . . 3
87abbii 2587 . 2
9 df-iin 4272 . 2
10 df-iin 4272 . 2
118, 9, 103eqtr4i 2503 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1452   wcel 1904  cab 2457  wnfc 2599  wral 2756  ciin 4270 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-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-iin 4272 This theorem is referenced by:  cbviinv  4309  elrfirn2  35609
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