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Theorem xp01disj 7165
 Description: Cartesian products with the singletons of ordinals 0 and 1 are disjoint. (Contributed by NM, 2-Jun-2007.)
Assertion
Ref Expression
xp01disj

Proof of Theorem xp01disj
StepHypRef Expression
1 1n0 7164 . . 3
21necomi 2727 . 2
3 xpsndisj 5435 . 2
42, 3ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395  =/=wne 2652  i^icin 3474   c0 3784  {csn 4029  X.cxp 5002   c1o 7142 This theorem is referenced by:  endisj  7624  uncdadom  8572  cdaun  8573  cdaen  8574  cda1dif  8577  pm110.643  8578  cdacomen  8582  cdaassen  8583  xpcdaen  8584  mapcdaen  8585  cdadom1  8587  infcda1  8594 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-eu 2286  df-mo 2287  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-br 4453  df-opab 4511  df-suc 4889  df-xp 5010  df-rel 5011  df-cnv 5012  df-1o 7149
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