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Theorem xpss2 4857
 Description: Subset relation for cross product. (Contributed by Jeff Hankins, 30-Aug-2009.)
Assertion
Ref Expression
xpss2 (A B → (C × A) (C × B))

Proof of Theorem xpss2
StepHypRef Expression
1 ssid 3290 . 2 C C
2 xpss12 4855 . 2 ((C C A B) → (C × A) (C × B))
31, 2mpan 651 1 (A B → (C × A) (C × B))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ⊆ wss 3257   × cxp 4770 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-opab 4623  df-xp 4784 This theorem is referenced by:  ssrnres  5059  fvfullfunlem3  5863
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