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Theorem ixpeq2 7078
 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 7077 . . 3
2 ss2ixp 7077 . . 3
31, 2anim12i 551 . 2
4 eqss 3365 . . . 4
54ralbii 2731 . . 3
6 r19.26 2840 . . 3
75, 6bitri 242 . 2
8 eqss 3365 . 2
93, 7, 83imtr4i 259 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653  wral 2707   wss 3322  cixp 7065 This theorem is referenced by:  ixpeq2dva  7079  ixpint  7091  prdsbas3  13705  pwsbas  13711  ptbasfi  17615  ptunimpt  17629  pttopon  17630  ptcld  17647  ptrescn  17673  ptuncnv  17841  ptunhmeo  17842  prdstotbnd  26505 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-in 3329  df-ss 3336  df-ixp 7066
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