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Theorem xpun 4600
 Description: The cross product of two unions. (Contributed by NM, 12-Aug-2004.)
Assertion
Ref Expression
xpun

Proof of Theorem xpun
StepHypRef Expression
1 xpundi 4595 . 2
2 xpundir 4596 . . 3
3 xpundir 4596 . . 3
42, 3uneq12i 3228 . 2
5 un4 3236 . 2
61, 4, 53eqtri 2164 1
 Colors of variables: wff set class Syntax hints:   wceq 1331   cun 3069   cxp 4537 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-opab 3990  df-xp 4545 This theorem is referenced by: (None)
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