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Theorem xpindir 5142
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 5140 . 2
2 inidm 3706 . . 3
32xpeq2i 5025 . 2
41, 3eqtr2i 2487 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  i^icin 3474  X.cxp 5002
This theorem is referenced by:  resres  5291  resindi  5294  imainrect  5453  resdmres  5503  cdaassen  8583  txhaus  20148  ustund  20724
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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511  df-xp 5010  df-rel 5011
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