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Theorem xpeq12d 4571
 Description: Equality deduction for Cartesian product. (Contributed by NM, 8-Dec-2013.)
Hypotheses
Ref Expression
xpeq1d.1
xpeq12d.2
Assertion
Ref Expression
xpeq12d

Proof of Theorem xpeq12d
StepHypRef Expression
1 xpeq1d.1 . 2
2 xpeq12d.2 . 2
3 xpeq12 4565 . 2
41, 2, 3syl2anc 409 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1332   cxp 4544 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-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  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-opab 3997  df-xp 4552 This theorem is referenced by:  sqxpeqd  4572  opeliunxp  4601  mpomptsx  6102  dmmpossx  6104  fmpox  6105  disjxp1  6140  erssxp  6459  cc2lem  7097  cc2  7098  fsum2dlemstep  11234  fisumcom2  11238  txbas  12464
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