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Theorem cbviin 4129
 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 2566 . . . 4
3 cbviun.2 . . . . 5
43nfcri 2566 . . . 4
5 cbviun.3 . . . . 5
65eleq2d 2503 . . . 4
72, 4, 6cbvral 2928 . . 3
87abbii 2548 . 2
9 df-iin 4096 . 2
10 df-iin 4096 . 2
118, 9, 103eqtr4i 2466 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  cab 2422  wnfc 2559  wral 2705  ciin 4094 This theorem is referenced by:  cbviinv  4131  elrfirn2  26750 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-iin 4096
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