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Theorem ixpeq1 7065
 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 5527 . . . 4
2 raleq 2896 . . . 4
31, 2anbi12d 692 . . 3
43abbidv 2549 . 2
5 dfixp 7057 . 2
6 dfixp 7057 . 2
74, 5, 63eqtr4g 2492 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  cab 2421  wral 2697   wfn 5441  cfv 5446  cixp 7055 This theorem is referenced by:  ixpeq1d  7066 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-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-fn 5449  df-ixp 7056
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