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Theorem ixpeq1 6614
 Description: Equality theorem for infinite Cartesian product. (Contributed by NM, 29-Sep-2006.)
Assertion
Ref Expression
ixpeq1
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem ixpeq1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fneq2 5223 . . . 4
2 raleq 2630 . . . 4
31, 2anbi12d 465 . . 3
43abbidv 2258 . 2
5 dfixp 6605 . 2
6 dfixp 6605 . 2
74, 5, 63eqtr4g 2198 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1332   wcel 1481  cab 2126  wral 2417   wfn 5129  cfv 5134  cixp 6603 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-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-fn 5137  df-ixp 6604 This theorem is referenced by:  ixpeq1d  6615
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