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Theorem xpindir 4727
 Description: Distributive law for cross product over intersection. Similar to Theorem 102 of [Suppes] p. 52. (Contributed by NM, 26-Sep-2004.)
Assertion
Ref Expression
xpindir

Proof of Theorem xpindir
StepHypRef Expression
1 inxp 4725 . 2
2 inidm 3285 . . 3
32xpeq2i 4617 . 2
41, 3eqtr2i 2274 1
 Colors of variables: wff set class Syntax hints:   wceq 1619   cin 3077   cxp 4578 This theorem is referenced by:  resres  4875  resindi  4878  imainrect  5026  resdmres  5070  cdaassen  7692  txhaus  17173 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-ral 2513  df-rex 2514  df-rab 2516  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553  df-opab 3975  df-xp 4594  df-rel 4595
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