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Theorem ixpeq2dva 7077
 Description: Equality theorem for infinite Cartesian product. (Contributed by Mario Carneiro, 11-Jun-2016.)
Hypothesis
Ref Expression
ixpeq2dva.1
Assertion
Ref Expression
ixpeq2dva
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem ixpeq2dva
StepHypRef Expression
1 ixpeq2dva.1 . . 3
21ralrimiva 2789 . 2
3 ixpeq2 7076 . 2
42, 3syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  wral 2705  cixp 7063 This theorem is referenced by:  ixpeq2dv  7078  dfac9  8016  xpsfrn2  13795  xpslem  13798  funcpropd  14097  natpropd  14173  prdsmgp  15716  elptr2  17606  dfac14  17650  xkoptsub  17686  prdsxmslem2  18559  prdsbnd2  26504 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-in 3327  df-ss 3334  df-ixp 7064
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