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Theorem xpindir 4958
 Description: Distributive law for Cartesian 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 4956 . 2
2 inidm 3648 . . 3
32xpeq2i 4844 . 2
41, 3eqtr2i 2432 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1405   cin 3413   cxp 4821 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-9 1846  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-sep 4517  ax-nul 4525  ax-pr 4630 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2759  df-rex 2760  df-rab 2763  df-v 3061  df-dif 3417  df-un 3419  df-in 3421  df-ss 3428  df-nul 3739  df-if 3886  df-sn 3973  df-pr 3975  df-op 3979  df-opab 4454  df-xp 4829  df-rel 4830 This theorem is referenced by:  resres  5106  resindi  5109  imainrect  5266  resdmres  5314  cdaassen  8594  txhaus  20440  ustund  21016
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