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Theorem xpeq12i 5026
 Description: Equality inference for Cartesian product. (Contributed by FL, 31-Aug-2009.)
Hypotheses
Ref Expression
xpeq12i.1
xpeq12i.2
Assertion
Ref Expression
xpeq12i

Proof of Theorem xpeq12i
StepHypRef Expression
1 xpeq12i.1 . 2
2 xpeq12i.2 . 2
3 xpeq12 5023 . 2
41, 2, 3mp2an 672 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395  X.cxp 5002 This theorem is referenced by:  xpssres  5313  imainrect  5453  cnvssrndm  5534  fpar  6904  canthwelem  9049  pjpm  18739  txbasval  20107  hausdiag  20146  ussval  20762  ex-xp  25157  ismgmOLD  25322  ghsubgolemOLD  25372  hh0oi  26822  idssxp  27469  fcnvgreu  27514  sitgclg  28284  isdrngo1  30359  trclubg  37785 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-opab 4511  df-xp 5010
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