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Theorem xpun 5062
Description: The Cartesian product of two unions. (Contributed by NM, 12-Aug-2004.)
Assertion
Ref Expression
xpun

Proof of Theorem xpun
StepHypRef Expression
1 xpundi 5057 . 2
2 xpundir 5058 . . 3
3 xpundir 5058 . . 3
42, 3uneq12i 3655 . 2
5 un4 3663 . 2
61, 4, 53eqtri 2490 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  u.cun 3473  X.cxp 5002
This theorem is referenced by:  ex-xp  25157
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-or 370  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-nfc 2607  df-v 3111  df-un 3480  df-opab 4511  df-xp 5010
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