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Theorem ixpeq2 7483
 Description: Equality theorem for infinite Cartesian product. (Contributed by NM, 29-Sep-2006.)
Assertion
Ref Expression
ixpeq2

Proof of Theorem ixpeq2
StepHypRef Expression
1 ss2ixp 7482 . . 3
2 ss2ixp 7482 . . 3
31, 2anim12i 566 . 2
4 eqss 3519 . . . 4
54ralbii 2895 . . 3
6 r19.26 2989 . . 3
75, 6bitri 249 . 2
8 eqss 3519 . 2
93, 7, 83imtr4i 266 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1379  wral 2814   wss 3476  cixp 7469 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ral 2819  df-in 3483  df-ss 3490  df-ixp 7470 This theorem is referenced by:  ixpeq2dva  7484  ixpint  7496  prdsbas3  14736  pwsbas  14742  ptbasfi  19845  ptunimpt  19859  pttopon  19860  ptcld  19877  ptrescn  19903  ptuncnv  20071  ptunhmeo  20072  ptrest  29653  prdstotbnd  29921
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