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Theorem xpeq2i 4866
Description: Equality inference for Cartesian product. (Contributed by NM, 21-Dec-2008.)
Hypothesis
Ref Expression
xpeq1i.1  |-  A  =  B
Assertion
Ref Expression
xpeq2i  |-  ( C  X.  A )  =  ( C  X.  B
)

Proof of Theorem xpeq2i
StepHypRef Expression
1 xpeq1i.1 . 2  |-  A  =  B
2 xpeq2 4860 . 2  |-  ( A  =  B  ->  ( C  X.  A )  =  ( C  X.  B
) )
31, 2ax-mp 5 1  |-  ( C  X.  A )  =  ( C  X.  B
)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1369    X. cxp 4843
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-opab 4356  df-xp 4851
This theorem is referenced by:  xpindir  4979  difxp1  5268  xpima  5285  xpexgALT  6575  curry1  6669  fparlem3  6679  fparlem4  6680  xp1en  7402  xp2cda  8354  xpcdaen  8357  pwcda1  8368  pwcdandom  8839  yonedalem3b  15094  yonedalem3  15095  pws1  16713  pwsmgp  16715  xkoinjcn  19265  imasdsf1olem  19953  zrdivrng  23924  df0op2  25161  ho01i  25237  nmop0h  25400  mbfmcst  26679  0rrv  26839  cvmlift2lem12  27208
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