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Theorem cbvixp 6616
 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 2295 . . . . 5
3 cbvixp.2 . . . . . 6
43nfel2 2295 . . . . 5
5 fveq2 5428 . . . . . 6
6 cbvixp.3 . . . . . 6
75, 6eleq12d 2211 . . . . 5
82, 4, 7cbvral 2653 . . . 4
98anbi2i 453 . . 3
109abbii 2256 . 2
11 dfixp 6601 . 2
12 dfixp 6601 . 2
1310, 11, 123eqtr4i 2171 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1332   wcel 1481  cab 2126  wnfc 2269  wral 2417   wfn 5125  cfv 5130  cixp 6599 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2691  df-un 3079  df-sn 3537  df-pr 3538  df-op 3540  df-uni 3744  df-br 3937  df-iota 5095  df-fn 5133  df-fv 5138  df-ixp 6600 This theorem is referenced by:  cbvixpv  6617  mptelixpg  6635
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