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Theorem cbvixp 7071
 Description: Change bound variable in an indexed Cartesian product. (Contributed by Jeff Madsen, 20-Jun-2011.)
Hypotheses
Ref Expression
cbvixp.1
cbvixp.2
cbvixp.3
Assertion
Ref Expression
cbvixp
Distinct variable group:   ,,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbvixp
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbvixp.1 . . . . . 6
21nfel2 2583 . . . . 5
3 cbvixp.2 . . . . . 6
43nfel2 2583 . . . . 5
5 fveq2 5720 . . . . . 6
6 cbvixp.3 . . . . . 6
75, 6eleq12d 2503 . . . . 5
82, 4, 7cbvral 2920 . . . 4
98anbi2i 676 . . 3
109abbii 2547 . 2
11 dfixp 7057 . 2
12 dfixp 7057 . 2
1310, 11, 123eqtr4i 2465 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  cab 2421  wnfc 2558  wral 2697   wfn 5441  cfv 5446  cixp 7055 This theorem is referenced by:  cbvixpv  7072  mptelixpg  7091  ixpiunwdom  7551  prdsbas3  13695  elptr2  17598  ptunimpt  17619  ptcldmpt  17638 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 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fn 5449  df-fv 5454  df-ixp 7056
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